diff --git a/CHANGELOG.md b/CHANGELOG.md
index 1c5b35bd0c197d..b1faaf6c5d325c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -35,6 +35,8 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 ### Deprecated
 
+- `period` has been deprecated in favor of `every_n_epochs` in the `ModelCheckpoint` callback ([#6146](https://github.com/PyTorchLightning/pytorch-lightning/pull/6146))
+
 
 ### Removed
 
diff --git a/pytorch_lightning/callbacks/model_checkpoint.py b/pytorch_lightning/callbacks/model_checkpoint.py
index 1ece791c89b96f..719892266231d9 100644
--- a/pytorch_lightning/callbacks/model_checkpoint.py
+++ b/pytorch_lightning/callbacks/model_checkpoint.py
@@ -174,8 +174,8 @@ def __init__(
         self.save_last = save_last
         self.save_top_k = save_top_k
         self.save_weights_only = save_weights_only
-        self.period = every_n_epochs
-        self.every_n_epochs = every_n_epochs
+        self.every_n_epochs = period or every_n_epochs
+        self.period = self.every_n_epochs
         self.every_n_batches = every_n_batches
         self._last_global_step_saved = -1
         self.current_score = None
@@ -192,8 +192,6 @@ def __init__(
                 'Argument `period` is deprecated in v1.3 and will be removed in v1.5.'
                 ' Please use `every_n_epochs` instead.', DeprecationWarning
             )
-            self.every_n_epochs = period
-            self.period = period
 
         self.__init_monitor_mode(monitor, mode)
         self.__init_ckpt_dir(dirpath, filename, save_top_k)
@@ -209,7 +207,7 @@ def on_pretrain_routine_start(self, trainer, pl_module):
     def on_train_batch_end(self, trainer, pl_module, outputs, batch, batch_idx, dataloader_idx) -> None:
         if self._should_skip_saving_checkpoint(trainer):
             return
-        step = trainer.global_step
+        step = trainer.total_batch_idx
         skip_batch = self.every_n_steps < 1 or ((step + 1) % self.every_n_steps != 0)
         if skip_batch:
             return
diff --git a/tests/checkpointing/test_model_checkpoint.py b/tests/checkpointing/test_model_checkpoint.py
index 4ea0a4d1a1de22..476850a995d34f 100644
--- a/tests/checkpointing/test_model_checkpoint.py
+++ b/tests/checkpointing/test_model_checkpoint.py
@@ -592,9 +592,8 @@ def test_model_checkpoint_every_n_epochs(tmpdir, every_n_epochs):
         default_root_dir=tmpdir,
         callbacks=[checkpoint_callback],
         max_epochs=epochs,
-        limit_train_batches=0.1,
-        limit_val_batches=0.1,
-        val_check_interval=1.0,
+        limit_train_batches=1,
+        limit_val_batches=1,
         logger=False,
     )
     trainer.fit(model)
@@ -615,9 +614,8 @@ def test_model_checkpoint_every_n_epochs_and_no_period(tmpdir, every_n_epochs):
         default_root_dir=tmpdir,
         callbacks=[checkpoint_callback],
         max_epochs=epochs,
-        limit_train_batches=0.1,
-        limit_val_batches=0.1,
-        val_check_interval=1.0,
+        limit_train_batches=1,
+        limit_val_batches=1,
         logger=False,
     )
     trainer.fit(model)
@@ -631,16 +629,15 @@ def test_ckpt_every_n_batches(tmpdir):
     """ Tests that the checkpoints are saved every n training steps. """
 
     model = LogInTwoMethods()
-
+    every_n_batches = 16
     trainer = Trainer(
         default_root_dir=tmpdir,
-        min_epochs=2,
         max_epochs=2,
         progress_bar_refresh_rate=0,
         checkpoint_callback=ModelCheckpoint(
             filename="{step}",
             every_n_epochs=0,
-            every_n_batches=16,
+            every_n_batches=every_n_batches,
             dirpath=tmpdir,
             save_top_k=-1,
             save_last=False,
@@ -649,16 +646,7 @@ def test_ckpt_every_n_batches(tmpdir):
     )
 
     trainer.fit(model)
-    expected = [
-        "step=15.ckpt",
-        "step=31.ckpt",
-        "step=47.ckpt",
-        "step=63.ckpt",
-        "step=79.ckpt",
-        "step=95.ckpt",
-        "step=111.ckpt",
-        "step=127.ckpt",
-    ]
+    expected=[f"step={i}.ckpt" for i in range(15, 128, every_n_batches)]
     assert set(os.listdir(tmpdir)) == set(expected)
 
 
@@ -667,9 +655,7 @@ def test_ckpt_every_n_batches_and_every_n_epochs(tmpdir):
     model = LogInTwoMethods()
     trainer = Trainer(
         default_root_dir=tmpdir,
-        min_epochs=2,
         max_epochs=2,
-        progress_bar_refresh_rate=0,
         checkpoint_callback=ModelCheckpoint(
             every_n_epochs=1,
             every_n_batches=30,