diff --git a/CHANGELOG.md b/CHANGELOG.md
index e5d266c77dfd8..f7b251939ce14 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -157,6 +157,9 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 - Use only a single instance of `rich.console.Console` throughout codebase ([#12886](https://github.com/PyTorchLightning/pytorch-lightning/pull/12886))
 
 
+- Fixed an issue to ensure all the checkpoint states are saved in a common filepath with `DeepspeedStrategy` ([#12887](https://github.com/PyTorchLightning/pytorch-lightning/pull/12887))
+
+
 ## [1.6.1] - 2022-04-13
 
 ### Changed
diff --git a/pytorch_lightning/strategies/deepspeed.py b/pytorch_lightning/strategies/deepspeed.py
index 7874322a4d74a..b6a353ae15e7b 100644
--- a/pytorch_lightning/strategies/deepspeed.py
+++ b/pytorch_lightning/strategies/deepspeed.py
@@ -762,6 +762,9 @@ def save_checkpoint(self, checkpoint: Dict, filepath: _PATH, storage_options: Op
             TypeError:
                 If ``storage_options`` arg is passed in
         """
+        # broadcast the filepath from rank 0 to ensure all the states are saved in a common filepath
+        filepath = self.broadcast(filepath)
+
         if storage_options is not None:
             raise TypeError(
                 "`Trainer.save_checkpoint(..., storage_options=...)` with `storage_options` arg"
diff --git a/tests/strategies/test_deepspeed_strategy.py b/tests/strategies/test_deepspeed_strategy.py
index 319289d200f4f..dd9bfcea236d2 100644
--- a/tests/strategies/test_deepspeed_strategy.py
+++ b/tests/strategies/test_deepspeed_strategy.py
@@ -1269,13 +1269,19 @@ def test_deepspeed_with_meta_device(tmpdir):
 def test_deepspeed_multi_save_same_filepath(tmpdir):
     """Test that verifies that deepspeed saves only latest checkpoint in the specified path and deletes the old
     sharded checkpoints."""
-    model = BoringModel()
+
+    class CustomModel(BoringModel):
+        def training_step(self, *args, **kwargs):
+            self.log("grank", self.global_rank)
+            return super().training_step(*args, **kwargs)
+
+    model = CustomModel()
     trainer = Trainer(
         default_root_dir=tmpdir,
         strategy="deepspeed",
         accelerator="gpu",
         devices=2,
-        callbacks=[ModelCheckpoint(save_top_k=1, save_last=True)],
+        callbacks=[ModelCheckpoint(filename="{epoch}_{step}_{grank}", save_top_k=1)],
         limit_train_batches=1,
         limit_val_batches=0,
         num_sanity_val_steps=0,
@@ -1284,9 +1290,14 @@ def test_deepspeed_multi_save_same_filepath(tmpdir):
         enable_model_summary=False,
     )
     trainer.fit(model)
-    ckpt_path = os.path.join(trainer.checkpoint_callback.dirpath, "last.ckpt")
-    expected = ["latest", "zero_to_fp32.py", "checkpoint"]
-    assert set(expected) == set(os.listdir(ckpt_path))
+
+    filepath = "epoch=1_step=2_grank=0.0.ckpt"
+    expected = {filepath}
+    assert expected == set(os.listdir(trainer.checkpoint_callback.dirpath))
+
+    ckpt_path = os.path.join(trainer.checkpoint_callback.dirpath, filepath)
+    expected = {"latest", "zero_to_fp32.py", "checkpoint"}
+    assert expected == set(os.listdir(ckpt_path))
 
 
 @RunIf(min_gpus=2, standalone=True, deepspeed=True)