diff --git a/src/operator/subgraph/build_subgraph.cc b/src/operator/subgraph/build_subgraph.cc
index 413395c3b74f..53c4d73a3537 100644
--- a/src/operator/subgraph/build_subgraph.cc
+++ b/src/operator/subgraph/build_subgraph.cc
@@ -226,9 +226,7 @@ bool LabelSubgraph(const nnvm::Graph& g, SubgraphSelectorV2Ptr subgraph_selector
     std::stack<const nnvm::Node*> s;
     s.push(descendant);
     size_t count = 0;
-    while (!s.empty()) {
-      CHECK_LT(count, indexed_graph.num_nodes()) << "Finding ancestor failed. There is probably"
-                                                    " a loop in the graph";
+    while (!s.empty() && count < indexed_graph.num_nodes()) {
       ++count;
       const nnvm::Node* top = s.top();
       s.pop();
@@ -276,10 +274,6 @@ bool LabelSubgraph(const nnvm::Graph& g, SubgraphSelectorV2Ptr subgraph_selector
 
   if (excluded_node_id != -1) {
     CHECK_LT(excluded_node_id, static_cast<int>(simple_nodes.size()));
-    CHECK_NE(excluded_node_id, static_cast<int>(snid))
-      << "A cycle is found in the computational graph between nodes "
-      << simple_nodes[excluded_node_id]->node->attrs.name << " and "
-      << simple_nodes[snid]->node->attrs.name;
     excluded_nodes->insert(simple_nodes[excluded_node_id].get());
     ResetNodeLabels(g, simple_nodes, subgraph_nodes);
     return false;
@@ -306,6 +300,7 @@ void PreSelectSubgraphNodes(const nnvm::Graph& g, SubgraphSelectorV2Ptr subgraph
                             const std::vector<BiDirectedNodePtr>& simple_nodes,
                             std::vector<BiDirectedNode*>* subgraph_nodes) {
   std::unordered_set<const BiDirectedNode*> excluded_nodes;
+  size_t n_excluded_nodes = 0;
   const size_t max_num_retry = simple_nodes.size() * simple_nodes.size();
   size_t count = 0;
   bool success = false;
@@ -313,7 +308,11 @@ void PreSelectSubgraphNodes(const nnvm::Graph& g, SubgraphSelectorV2Ptr subgraph
     success = LabelSubgraph(g, subgraph_selector, label, snid, simple_nodes, subgraph_nodes,
                             &excluded_nodes);
     if (!success) {
-      CHECK(!excluded_nodes.empty());
+      if (excluded_nodes.size() == n_excluded_nodes) {
+        // no possible subgraph for the current node snid
+        break;
+      }
+      n_excluded_nodes = excluded_nodes.size();
       std::string excluded_node_names;
       for (auto node : excluded_nodes) {
         excluded_node_names += node->node->attrs.name + ", ";