diff --git a/pkg/ddl/executor.go b/pkg/ddl/executor.go
index da51fc979de5b..b7906ad09af8a 100644
--- a/pkg/ddl/executor.go
+++ b/pkg/ddl/executor.go
@@ -958,10 +958,6 @@ func checkGlobalIndex(ec errctx.Context, tblInfo *model.TableInfo, indexInfo *mo
 			// partitioning an index differently from the table partitioning.
 			return dbterror.ErrGeneralUnsupportedDDL.GenWithStackByArgs("Global Index on non-partitioned table")
 		}
-		// TODO: remove limitation
-		if !indexInfo.Unique {
-			return dbterror.ErrGeneralUnsupportedDDL.GenWithStackByArgs("GLOBAL IndexOption on non-unique index")
-		}
 		validateGlobalIndexWithGeneratedColumns(ec, tblInfo, indexInfo.Name.O, indexInfo.Columns)
 	}
 	return nil
@@ -4543,15 +4539,11 @@ func GetName4AnonymousIndex(t table.Table, colName pmodel.CIStr, idxName pmodel.
 	return indexName
 }
 
-func checkCreateUniqueGlobalIndex(ec errctx.Context, tblInfo *model.TableInfo, indexName string, indexColumns []*model.IndexColumn, isUnique bool, isGlobal bool) error {
+func checkCreateGlobalIndex(ec errctx.Context, tblInfo *model.TableInfo, indexName string, indexColumns []*model.IndexColumn, isUnique bool, isGlobal bool) error {
 	pi := tblInfo.GetPartitionInfo()
 	if isGlobal && pi == nil {
 		return dbterror.ErrGeneralUnsupportedDDL.GenWithStackByArgs("Global Index on non-partitioned table")
 	}
-	if isGlobal && !isUnique {
-		// TODO: remove this limitation
-		return dbterror.ErrGeneralUnsupportedDDL.GenWithStackByArgs("Global IndexOption on non-unique index")
-	}
 	if isUnique && pi != nil {
 		ck, err := checkPartitionKeysConstraint(tblInfo.GetPartitionInfo(), indexColumns, tblInfo)
 		if err != nil {
@@ -4561,6 +4553,8 @@ func checkCreateUniqueGlobalIndex(ec errctx.Context, tblInfo *model.TableInfo, i
 			// index columns does not contain all partition columns, must be global
 			return dbterror.ErrGlobalIndexNotExplicitlySet.GenWithStackByArgs(indexName)
 		}
+	}
+	if isGlobal {
 		validateGlobalIndexWithGeneratedColumns(ec, tblInfo, indexName, indexColumns)
 	}
 	return nil
@@ -4611,7 +4605,7 @@ func (e *executor) CreatePrimaryKey(ctx sessionctx.Context, ti ast.Ident, indexN
 		return err
 	}
 
-	if err = checkCreateUniqueGlobalIndex(ctx.GetSessionVars().StmtCtx.ErrCtx(), tblInfo, "PRIMARY", indexColumns, true, indexOption != nil && indexOption.Global); err != nil {
+	if err = checkCreateGlobalIndex(ctx.GetSessionVars().StmtCtx.ErrCtx(), tblInfo, "PRIMARY", indexColumns, true, indexOption != nil && indexOption.Global); err != nil {
 		return err
 	}
 
@@ -4879,7 +4873,7 @@ func (e *executor) createIndex(ctx sessionctx.Context, ti ast.Ident, keyType ast
 		return errors.Trace(err)
 	}
 
-	if err = checkCreateUniqueGlobalIndex(ctx.GetSessionVars().StmtCtx.ErrCtx(), tblInfo, indexName.O, indexColumns, unique, indexOption != nil && indexOption.Global); err != nil {
+	if err = checkCreateGlobalIndex(ctx.GetSessionVars().StmtCtx.ErrCtx(), tblInfo, indexName.O, indexColumns, unique, indexOption != nil && indexOption.Global); err != nil {
 		return err
 	}
 
diff --git a/pkg/ddl/index_modify_test.go b/pkg/ddl/index_modify_test.go
index f7b503ca7d15a..9bb9c6f859af2 100644
--- a/pkg/ddl/index_modify_test.go
+++ b/pkg/ddl/index_modify_test.go
@@ -749,6 +749,39 @@ func TestAddGlobalIndex(t *testing.T) {
 
 	require.NoError(t, txn.Commit(context.Background()))
 
+	// Test add non-unqiue global index
+	tk.MustExec("drop table if exists test_t2")
+	tk.MustExec("create table test_t2 (a int, b int) partition by range (b)" +
+		" (partition p0 values less than (10), " +
+		"  partition p1 values less than (maxvalue));")
+	tk.MustExec("insert test_t2 values (2, 1)")
+	tk.MustExec("alter table test_t2 add key p_a (a) global")
+	tk.MustExec("insert test_t2 values (1, 11)")
+	tbl = external.GetTableByName(t, tk, "test", "test_t2")
+	tblInfo = tbl.Meta()
+	indexInfo = tblInfo.FindIndexByName("p_a")
+	require.NotNil(t, indexInfo)
+	require.True(t, indexInfo.Global)
+	require.False(t, indexInfo.Unique)
+
+	require.NoError(t, sessiontxn.NewTxn(context.Background(), tk.Session()))
+	txn, err = tk.Session().Txn(true)
+	require.NoError(t, err)
+
+	// check row 1
+	pid = tblInfo.Partition.Definitions[0].ID
+	idxVals = []types.Datum{types.NewDatum(2)}
+	rowVals = []types.Datum{types.NewDatum(2), types.NewDatum(1)}
+	checkGlobalIndexRow(t, tk.Session(), tblInfo, indexInfo, pid, idxVals, rowVals)
+
+	// check row 2
+	pid = tblInfo.Partition.Definitions[1].ID
+	idxVals = []types.Datum{types.NewDatum(1)}
+	rowVals = []types.Datum{types.NewDatum(1), types.NewDatum(11)}
+	checkGlobalIndexRow(t, tk.Session(), tblInfo, indexInfo, pid, idxVals, rowVals)
+
+	require.NoError(t, txn.Commit(context.Background()))
+
 	// `sanity_check.go` will check the del_range numbers are correct or not.
 	// normal index
 	tk.MustExec("drop table if exists t")
@@ -801,7 +834,17 @@ func checkGlobalIndexRow(
 	require.NoError(t, err)
 	key := tablecodec.EncodeIndexSeekKey(tblInfo.ID, indexInfo.ID, encodedValue)
 	require.NoError(t, err)
-	value, err := txn.Get(context.Background(), key)
+	var value []byte
+	if indexInfo.Unique {
+		value, err = txn.Get(context.Background(), key)
+	} else {
+		var iter kv.Iterator
+		iter, err = txn.Iter(key, key.PrefixNext())
+		require.NoError(t, err)
+		require.True(t, iter.Valid())
+		key = iter.Key()
+		value = iter.Value()
+	}
 	require.NoError(t, err)
 	idxColInfos := tables.BuildRowcodecColInfoForIndexColumns(indexInfo, tblInfo)
 	colVals, err := tablecodec.DecodeIndexKV(key, value, len(indexInfo.Columns), tablecodec.HandleDefault, idxColInfos)
diff --git a/pkg/ddl/ingest/integration_test.go b/pkg/ddl/ingest/integration_test.go
index 2aba4f018354e..c2a3dd5c4ad8e 100644
--- a/pkg/ddl/ingest/integration_test.go
+++ b/pkg/ddl/ingest/integration_test.go
@@ -494,6 +494,15 @@ func TestAddGlobalIndexInIngest(t *testing.T) {
 	require.Greater(t, len(rsGlobalIndex1.Rows()), len(rsGlobalIndex.Rows()))
 	require.Equal(t, rsGlobalIndex1.String(), rsTable.String())
 	require.Equal(t, rsGlobalIndex1.String(), rsGlobalIndex2.String())
+
+	// for non-unique global idnexes
+	tk.MustExec("alter table t add index idx_7(b) global, add index idx_8(b) global")
+	rsNonUniqueGlobalIndex1 := tk.MustQuery("select * from t use index(idx_7)").Sort()
+	rsTable = tk.MustQuery("select * from t use index()").Sort()
+	rsNonUniqueGlobalIndex2 := tk.MustQuery("select * from t use index(idx_8)").Sort()
+	require.Greater(t, len(rsNonUniqueGlobalIndex1.Rows()), len(rsGlobalIndex.Rows()))
+	require.Equal(t, rsNonUniqueGlobalIndex1.String(), rsTable.String())
+	require.Equal(t, rsNonUniqueGlobalIndex1.String(), rsNonUniqueGlobalIndex2.String())
 }
 
 func TestAddGlobalIndexInIngestWithUpdate(t *testing.T) {
diff --git a/pkg/ddl/partition.go b/pkg/ddl/partition.go
index 80902fe4a37cd..bf3159e5805ad 100644
--- a/pkg/ddl/partition.go
+++ b/pkg/ddl/partition.go
@@ -3244,28 +3244,18 @@ func (w *worker) onReorganizePartition(jobCtx *jobContext, job *model.Job) (ver
 				// When removing partitioning, set all indexes to 'local' since it will become a non-partitioned table!
 				newGlobal = false
 			}
-			if !index.Unique {
-				// for now, only unique index can be global, non-unique indexes are 'local'
-				// TODO: For the future loosen this restriction and allow non-unique global indexes
-				if newGlobal {
-					job.State = model.JobStateCancelled
-					return ver, dbterror.ErrGeneralUnsupportedDDL.GenWithStackByArgs(fmt.Sprintf("PARTITION BY, index '%v' is not unique, but has Global Index set", index.Name.O))
-				}
+			if !index.Global && !newGlobal {
 				continue
 			}
 			inAllPartitionColumns, err := checkPartitionKeysConstraint(partInfo, index.Columns, tblInfo)
 			if err != nil {
 				return ver, errors.Trace(err)
 			}
-			// Currently only support Explicit Global indexes.
-			if !inAllPartitionColumns && !newGlobal {
+			// Currently only support Explicit Global indexes for unique index.
+			if !inAllPartitionColumns && !newGlobal && index.Unique {
 				job.State = model.JobStateCancelled
 				return ver, dbterror.ErrGlobalIndexNotExplicitlySet.GenWithStackByArgs(index.Name.O)
 			}
-			if !index.Global && !newGlobal {
-				// still local index, no need to duplicate index.
-				continue
-			}
 			if tblInfo.Partition.DDLChangedIndex == nil {
 				tblInfo.Partition.DDLChangedIndex = make(map[int64]bool)
 			}
@@ -3400,7 +3390,7 @@ func (w *worker) onReorganizePartition(jobCtx *jobContext, job *model.Job) (ver
 		}
 
 		for i := range tblInfo.Indices {
-			if tblInfo.Indices[i].Unique && tblInfo.Indices[i].State == model.StateDeleteOnly {
+			if tblInfo.Indices[i].State == model.StateDeleteOnly {
 				tblInfo.Indices[i].State = model.StateWriteOnly
 			}
 		}
@@ -3420,7 +3410,7 @@ func (w *worker) onReorganizePartition(jobCtx *jobContext, job *model.Job) (ver
 		// so that new data will be updated in both old and new partitions when reorganizing.
 		job.SnapshotVer = 0
 		for i := range tblInfo.Indices {
-			if tblInfo.Indices[i].Unique && tblInfo.Indices[i].State == model.StateWriteOnly {
+			if tblInfo.Indices[i].State == model.StateWriteOnly {
 				tblInfo.Indices[i].State = model.StateWriteReorganization
 			}
 		}
@@ -3462,9 +3452,6 @@ func (w *worker) onReorganizePartition(jobCtx *jobContext, job *model.Job) (ver
 		})
 
 		for _, index := range tblInfo.Indices {
-			if !index.Unique {
-				continue
-			}
 			isNew, ok := tblInfo.Partition.DDLChangedIndex[index.ID]
 			if !ok {
 				continue
@@ -3564,8 +3551,8 @@ func (w *worker) onReorganizePartition(jobCtx *jobContext, job *model.Job) (ver
 
 		var dropIndices []*model.IndexInfo
 		for _, indexInfo := range tblInfo.Indices {
-			if indexInfo.Unique && indexInfo.State == model.StateDeleteOnly {
-				// Drop the old unique (possible global) index, see onDropIndex
+			if indexInfo.State == model.StateDeleteOnly {
+				// Drop the old indexes, see onDropIndex
 				indexInfo.State = model.StateNone
 				DropIndexColumnFlag(tblInfo, indexInfo)
 				RemoveDependentHiddenColumns(tblInfo, indexInfo)
diff --git a/tests/integrationtest/r/globalindex/ddl.result b/tests/integrationtest/r/globalindex/ddl.result
index 735d7856b1a03..0b4bbdac32471 100644
--- a/tests/integrationtest/r/globalindex/ddl.result
+++ b/tests/integrationtest/r/globalindex/ddl.result
@@ -5,39 +5,11 @@ Error 8200 (HY000): Unsupported Global Index on non-partitioned table
 create table t (a int, b int, unique index idx(a) global) partition by hash(b) partitions 3;
 drop table t;
 create table t (a int, b int, index idx(a) global) partition by hash(b) partitions 3;
-Error 8200 (HY000): Unsupported GLOBAL IndexOption on non-unique index
+drop table t;
 create table t3(a int not null, b int, primary key(a) nonclustered, unique idx_b(b) global) partition by hash(a) partitions 3;
 drop table t3;
 create table t (a int primary key nonclustered, b int) partition by hash(b) partitions 3;
 Error 8264 (HY000): Global Index is needed for index 'PRIMARY', since the unique index is not including all partitioning columns, and GLOBAL is not given as IndexOption
-create table t (a int, b int, unique key (a)) partition by hash(a) partitions 3;
-alter table t partition by hash(b) partitions 3;
-Error 8264 (HY000): Global Index is needed for index 'a', since the unique index is not including all partitioning columns, and GLOBAL is not given as IndexOption
-alter table t partition by hash(b) partitions 3 update indexes (a global);
-alter table t add index idxErr (b) global;
-Error 8200 (HY000): Unsupported Global IndexOption on non-unique index
-alter table t add unique index idxOK (b) global;
-create index idxErr on t (b) global;
-Error 8200 (HY000): Unsupported Global IndexOption on non-unique index
-create unique index idxOK2 on t (b) global;
-alter table t remove partitioning;
-alter table t add index idxErr (b) global;
-Error 8200 (HY000): Unsupported Global Index on non-partitioned table
-alter table t add unique index idxErr (b) global;
-Error 8200 (HY000): Unsupported Global Index on non-partitioned table
-create index idxErr on t (b) global;
-Error 8200 (HY000): Unsupported Global Index on non-partitioned table
-create unique index idxErr on t (b) global;
-Error 8200 (HY000): Unsupported Global Index on non-partitioned table
-drop table t;
-create table t (a int, b int, unique index idx(a) global);
-Error 8200 (HY000): Unsupported Global Index on non-partitioned table
-create table t (a int, b int, index idx(a) global);
-Error 8200 (HY000): Unsupported Global Index on non-partitioned table
-create table t (a int, b int, index idx(a) global) partition by hash(b) partitions 3;
-Error 8200 (HY000): Unsupported GLOBAL IndexOption on non-unique index
-create table t (a int not null, b int, primary key(a) nonclustered, unique idx_b(b) global) partition by hash(a) partitions 3;
-drop table t;
 create table t (a int key global, b int) partition by hash(b) partitions 3;
 Error 8200 (HY000): Unsupported create an index that is both a global index and a clustered index
 create table t (a int unique, b int) partition by hash(b) partitions 3;
@@ -65,14 +37,34 @@ create table t (a int, b int, unique key (a)) partition by hash(a) partitions 3;
 alter table t partition by hash(b) partitions 3;
 Error 8264 (HY000): Global Index is needed for index 'a', since the unique index is not including all partitioning columns, and GLOBAL is not given as IndexOption
 alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a GLOBAL);
+alter table t add index idxOK (b) global;
+alter table t add unique index idxOK2 (a) global;
+alter table t add unique index idxOK3 (b) global;
+create index idxOK4 on t (b) global;
+create unique index idxOK5 on t (a) global;
+create unique index idxOK6 on t (b) global;
+alter table t remove partitioning;
+show create table t;
+Table	Create Table
+t	CREATE TABLE `t` (
+  `a` int DEFAULT NULL,
+  `b` int DEFAULT NULL,
+  UNIQUE KEY `a` (`a`),
+  KEY `idxOK` (`b`),
+  UNIQUE KEY `idxOK2` (`a`),
+  UNIQUE KEY `idxOK3` (`b`),
+  KEY `idxOK4` (`b`),
+  UNIQUE KEY `idxOK5` (`a`),
+  UNIQUE KEY `idxOK6` (`b`)
+) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin
 alter table t add index idxErr (b) global;
-Error 8200 (HY000): Unsupported Global IndexOption on non-unique index
-alter table t add unique index idxOK (a) global;
-alter table t add unique index idxOK2 (b) global;
+Error 8200 (HY000): Unsupported Global Index on non-partitioned table
+alter table t add unique index idxErr (b) global;
+Error 8200 (HY000): Unsupported Global Index on non-partitioned table
 create index idxErr on t (b) global;
-Error 8200 (HY000): Unsupported Global IndexOption on non-unique index
-create unique index idxOK3 on t (a) global;
-create unique index idxOK4 on t (b) global;
+Error 8200 (HY000): Unsupported Global Index on non-partitioned table
+create unique index idxErr on t (b) global;
+Error 8200 (HY000): Unsupported Global Index on non-partitioned table
 drop table t;
 create table t(a int, b int, primary key (a) nonclustered global);
 Error 8200 (HY000): Unsupported Global Index on non-partitioned table
@@ -82,6 +74,72 @@ create table t(a int, b int, primary key (a) global) partition by hash(a) partit
 Error 8200 (HY000): Unsupported create an index that is both a global index and a clustered index
 create table t(a int, b int, primary key (b) global) partition by hash(a) partitions 5;
 Error 8200 (HY000): Unsupported create an index that is both a global index and a clustered index
+create table t(a int, b int, key(a), key(b)) partition by hash(a) partitions 4;
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a GLOBAL, b LOCAL);
+show create table t;
+Table	Create Table
+t	CREATE TABLE `t` (
+  `a` int DEFAULT NULL,
+  `b` int DEFAULT NULL,
+  KEY `b` (`b`),
+  KEY `a` (`a`) /*T![global_index] GLOBAL */
+) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin
+PARTITION BY HASH (`b`) PARTITIONS 3
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a GLOBAL, b GLOBAL);
+show create table t;
+Table	Create Table
+t	CREATE TABLE `t` (
+  `a` int DEFAULT NULL,
+  `b` int DEFAULT NULL,
+  KEY `b` (`b`) /*T![global_index] GLOBAL */,
+  KEY `a` (`a`) /*T![global_index] GLOBAL */
+) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin
+PARTITION BY HASH (`b`) PARTITIONS 3
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a LOCAL);
+show create table t;
+Table	Create Table
+t	CREATE TABLE `t` (
+  `a` int DEFAULT NULL,
+  `b` int DEFAULT NULL,
+  KEY `b` (`b`) /*T![global_index] GLOBAL */,
+  KEY `a` (`a`)
+) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin
+PARTITION BY HASH (`b`) PARTITIONS 3
+drop table t;
+create table t(a int, b int, unique key(a), unique key(b) global) partition by hash(a) partitions 4;
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a GLOBAL, b LOCAL);
+show create table t;
+Table	Create Table
+t	CREATE TABLE `t` (
+  `a` int DEFAULT NULL,
+  `b` int DEFAULT NULL,
+  UNIQUE KEY `a` (`a`) /*T![global_index] GLOBAL */,
+  UNIQUE KEY `b` (`b`)
+) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin
+PARTITION BY HASH (`b`) PARTITIONS 3
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a GLOBAL, b GLOBAL);
+show create table t;
+Table	Create Table
+t	CREATE TABLE `t` (
+  `a` int DEFAULT NULL,
+  `b` int DEFAULT NULL,
+  UNIQUE KEY `a` (`a`) /*T![global_index] GLOBAL */,
+  UNIQUE KEY `b` (`b`) /*T![global_index] GLOBAL */
+) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin
+PARTITION BY HASH (`b`) PARTITIONS 3
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a LOCAL);
+Error 8264 (HY000): Global Index is needed for index 'a', since the unique index is not including all partitioning columns, and GLOBAL is not given as IndexOption
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (b LOCAL);
+show create table t;
+Table	Create Table
+t	CREATE TABLE `t` (
+  `a` int DEFAULT NULL,
+  `b` int DEFAULT NULL,
+  UNIQUE KEY `a` (`a`) /*T![global_index] GLOBAL */,
+  UNIQUE KEY `b` (`b`)
+) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin
+PARTITION BY HASH (`b`) PARTITIONS 3
+drop table t;
 create table t(a int, b int);
 alter table t add primary key (a) global;
 Error 8200 (HY000): Unsupported Global Index on non-partitioned table
diff --git a/tests/integrationtest/r/globalindex/expression_index.result b/tests/integrationtest/r/globalindex/expression_index.result
index d8460fd4d771b..ec2a175682e79 100644
--- a/tests/integrationtest/r/globalindex/expression_index.result
+++ b/tests/integrationtest/r/globalindex/expression_index.result
@@ -40,3 +40,13 @@ Projection	3333.33	root	NULL	globalindex__expression_index.t.a, globalindex__exp
 select * from t partition(p0) use index(idx) where lower(b) > 'c';
 a	b
 5	x
+drop table if exists t;
+CREATE TABLE `t` (
+`a` int DEFAULT NULL,
+`b` char DEFAULT NULL,
+KEY `idx` ((lower(`b`))) global
+) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin
+PARTITION BY HASH (`a`) PARTITIONS 5;
+show warnings;
+Level	Code	Message
+Warning	8265	Auto analyze is not effective for index 'idx', need analyze manually
diff --git a/tests/integrationtest/r/globalindex/insert.result b/tests/integrationtest/r/globalindex/insert.result
index e873815ea20ff..94bf8a12a5359 100644
--- a/tests/integrationtest/r/globalindex/insert.result
+++ b/tests/integrationtest/r/globalindex/insert.result
@@ -10,3 +10,20 @@ select * from t use index (idx1) order by a desc;
 a	b
 2	5
 1	3
+drop table if exists t;
+create table t(a int, b int, index idx(a) global) partition by hash(b) partitions 5;
+insert into t values (1, 1), (1, 2), (2, 2);
+select * from t use index (idx);
+a	b
+1	1
+1	2
+2	2
+alter table t add index idx1(b) global;
+insert into t values (2, 4), (3, 4);
+select * from t use index (idx1) order by a desc, b;
+a	b
+3	4
+2	2
+2	4
+1	1
+1	2
diff --git a/tests/integrationtest/r/globalindex/update.result b/tests/integrationtest/r/globalindex/update.result
index 6a138c912af1c..8ae79d047ba9f 100644
--- a/tests/integrationtest/r/globalindex/update.result
+++ b/tests/integrationtest/r/globalindex/update.result
@@ -60,3 +60,14 @@ replace into t values ('',826536 );
 select * from t;
 a	b
 	826536
+drop table t;
+create table t(a int, b int, index idx(a) global) partition by hash(b) partitions 5;
+insert into t values (1, 2), (1, 3), (1, 4);
+replace into t values (2, 3);
+update t set a = 3, b = 4 where a = 1;
+select * from t;
+a	b
+2	3
+3	4
+3	4
+3	4
diff --git a/tests/integrationtest/t/globalindex/ddl.test b/tests/integrationtest/t/globalindex/ddl.test
index 3fcbb99f503aa..6807370d228d8 100644
--- a/tests/integrationtest/t/globalindex/ddl.test
+++ b/tests/integrationtest/t/globalindex/ddl.test
@@ -4,41 +4,13 @@ create table t (a int, b int, unique index idx(a) global);
 create table t (a int, b int, index idx(a) global);
 create table t (a int, b int, unique index idx(a) global) partition by hash(b) partitions 3;
 drop table t;
--- error 8200
 create table t (a int, b int, index idx(a) global) partition by hash(b) partitions 3;
+drop table t;
 create table t3(a int not null, b int, primary key(a) nonclustered, unique idx_b(b) global) partition by hash(a) partitions 3;
 drop table t3;
 -- error 8264
 create table t (a int primary key nonclustered, b int) partition by hash(b) partitions 3;
-create table t (a int, b int, unique key (a)) partition by hash(a) partitions 3;
--- error 8264
-alter table t partition by hash(b) partitions 3;
-alter table t partition by hash(b) partitions 3 update indexes (a global);
--- error 8200
-alter table t add index idxErr (b) global;
-alter table t add unique index idxOK (b) global;
--- error 8200
-create index idxErr on t (b) global;
-create unique index idxOK2 on t (b) global;
-alter table t remove partitioning;
--- error 8200
-alter table t add index idxErr (b) global;
--- error 8200
-alter table t add unique index idxErr (b) global;
--- error 8200
-create index idxErr on t (b) global;
--- error 8200
-create unique index idxErr on t (b) global;
-drop table t;
 
--- error 8200
-create table t (a int, b int, unique index idx(a) global);
--- error 8200
-create table t (a int, b int, index idx(a) global);
--- error 8200
-create table t (a int, b int, index idx(a) global) partition by hash(b) partitions 3;
-create table t (a int not null, b int, primary key(a) nonclustered, unique idx_b(b) global) partition by hash(a) partitions 3;
-drop table t;
 -- error 8200
 create table t (a int key global, b int) partition by hash(b) partitions 3;
 -- error 8264
@@ -47,6 +19,7 @@ create table t (a int unique, b int) partition by hash(b) partitions 3;
 create table t (a int unique key, b int) partition by hash(b) partitions 3;
 -- error 8264
 create table t (a int primary key nonclustered, b int) partition by hash(b) partitions 3;
+
 CREATE TABLE `t` (
   `a` int(11) NOT NULL,
   `b` int(11) DEFAULT NULL,
@@ -55,20 +28,30 @@ CREATE TABLE `t` (
 PARTITION BY HASH (`b`) PARTITIONS 3;
 show create table t;
 drop table t;
+
 create table t (a int, b int, unique key (a)) partition by hash(a) partitions 3;
 -- error 8264
 alter table t partition by hash(b) partitions 3;
 alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a GLOBAL);
+alter table t add index idxOK (b) global;
+alter table t add unique index idxOK2 (a) global;
+alter table t add unique index idxOK3 (b) global;
+create index idxOK4 on t (b) global;
+create unique index idxOK5 on t (a) global;
+create unique index idxOK6 on t (b) global;
+
+alter table t remove partitioning;
+show create table t;
 -- error 8200
 alter table t add index idxErr (b) global;
-alter table t add unique index idxOK (a) global;
-alter table t add unique index idxOK2 (b) global;
+-- error 8200
+alter table t add unique index idxErr (b) global;
 -- error 8200
 create index idxErr on t (b) global;
-create unique index idxOK3 on t (a) global;
-create unique index idxOK4 on t (b) global;
-
+-- error 8200
+create unique index idxErr on t (b) global;
 drop table t;
+
 --error 8200
 create table t(a int, b int, primary key (a) nonclustered global);
 --error 8200
@@ -78,6 +61,26 @@ create table t(a int, b int, primary key (a) global) partition by hash(a) partit
 --error 8200
 create table t(a int, b int, primary key (b) global) partition by hash(a) partitions 5;
 
+create table t(a int, b int, key(a), key(b)) partition by hash(a) partitions 4;
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a GLOBAL, b LOCAL);
+show create table t;
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a GLOBAL, b GLOBAL);
+show create table t;
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a LOCAL);
+show create table t;
+drop table t;
+
+create table t(a int, b int, unique key(a), unique key(b) global) partition by hash(a) partitions 4;
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a GLOBAL, b LOCAL);
+show create table t;
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a GLOBAL, b GLOBAL);
+show create table t;
+--error 8264
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (a LOCAL);
+alter table t partition by hash(b) partitions 3 UPDATE INDEXES (b LOCAL);
+show create table t;
+drop table t;
+
 create table t(a int, b int);
 --error 8200
 alter table t add primary key (a) global;
diff --git a/tests/integrationtest/t/globalindex/expression_index.test b/tests/integrationtest/t/globalindex/expression_index.test
index de5d36dc1ab2f..52ec1761502ba 100644
--- a/tests/integrationtest/t/globalindex/expression_index.test
+++ b/tests/integrationtest/t/globalindex/expression_index.test
@@ -23,3 +23,15 @@ select * from t use index(idx) where lower(b) > 'c' order by lower(b);
 explain format='brief' select * from t partition(p0) use index(idx) where lower(b) > 'c';
 select * from t partition(p0) use index(idx) where lower(b) > 'c';
 
+
+# For global index + non-unique index
+drop table if exists t;
+CREATE TABLE `t` (
+  `a` int DEFAULT NULL,
+  `b` char DEFAULT NULL,
+  KEY `idx` ((lower(`b`))) global
+) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin
+PARTITION BY HASH (`a`) PARTITIONS 5;
+
+show warnings;
+
diff --git a/tests/integrationtest/t/globalindex/insert.test b/tests/integrationtest/t/globalindex/insert.test
index 9e641354a341c..cb7457680fee7 100644
--- a/tests/integrationtest/t/globalindex/insert.test
+++ b/tests/integrationtest/t/globalindex/insert.test
@@ -8,3 +8,12 @@ insert into t values (2, 4), (3, 4) on duplicate key update a=2, b=5;
 select * from t use index (idx1) order by a desc;
 
 
+# Test global index + non-unique index
+drop table if exists t;
+create table t(a int, b int, index idx(a) global) partition by hash(b) partitions 5;
+insert into t values (1, 1), (1, 2), (2, 2);
+select * from t use index (idx);
+
+alter table t add index idx1(b) global;
+insert into t values (2, 4), (3, 4);
+select * from t use index (idx1) order by a desc, b;
diff --git a/tests/integrationtest/t/globalindex/update.test b/tests/integrationtest/t/globalindex/update.test
index e383f37f589d6..8a026ba854316 100644
--- a/tests/integrationtest/t/globalindex/update.test
+++ b/tests/integrationtest/t/globalindex/update.test
@@ -43,3 +43,14 @@ create table t(a varchar(70), b mediumint(9), unique index idx_a(a) global, uniq
 insert into t values ('',826534 );
 replace into t values ('',826536 );
 select * from t;
+
+# For global index + non-unique index
+drop table t;
+create table t(a int, b int, index idx(a) global) partition by hash(b) partitions 5;
+insert into t values (1, 2), (1, 3), (1, 4);
+
+# Replace will not affects, `idx` is a non-unique index.
+replace into t values (2, 3);
+update t set a = 3, b = 4 where a = 1;
+--sorted_result
+select * from t;