diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7c19a41a64..6b5ddef3e0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -284,6 +284,9 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 - Pass the `stage` argument of `Callback.{setup,teardown}` as a keyword ([#7973](https://github.com/PyTorchLightning/pytorch-lightning/pull/7973))
 
 
+- Fixed move best score to device in EarlyStopping Callback ([#7959](https://github.com/PyTorchLightning/pytorch-lightning/pull/7959))
+
+
 ## [1.3.6] - 2021-06-15
 
 ### Fixed
diff --git a/pytorch_lightning/callbacks/early_stopping.py b/pytorch_lightning/callbacks/early_stopping.py
index e40bb7180c..b6bff43fd6 100644
--- a/pytorch_lightning/callbacks/early_stopping.py
+++ b/pytorch_lightning/callbacks/early_stopping.py
@@ -196,7 +196,7 @@ class EarlyStopping(Callback):
         # when in dev debugging
         trainer.dev_debugger.track_early_stopping_history(self, current)
 
-        should_stop, reason = self._evalute_stopping_criteria(current)
+        should_stop, reason = self._evalute_stopping_criteria(current, trainer)
 
         # stop every ddp process if any world process decides to stop
         should_stop = trainer.training_type_plugin.reduce_boolean_decision(should_stop)
@@ -206,7 +206,7 @@ class EarlyStopping(Callback):
         if reason and self.verbose:
             self._log_info(trainer, reason)
 
-    def _evalute_stopping_criteria(self, current: torch.Tensor) -> Tuple[bool, str]:
+    def _evalute_stopping_criteria(self, current: torch.Tensor, trainer: 'pl.Trainer') -> Tuple[bool, str]:
         should_stop = False
         reason = None
         if self.check_finite and not torch.isfinite(current):
@@ -229,7 +229,7 @@ class EarlyStopping(Callback):
                 f" {self.monitor} = {current} {self.order_dict[self.mode]} {self.divergence_threshold}."
                 " Signaling Trainer to stop."
             )
-        elif self.monitor_op(current - self.min_delta, self.best_score):
+        elif self.monitor_op(current - self.min_delta, self.best_score.to(trainer.lightning_module.device)):
             should_stop = False
             reason = self._improvement_message(current)
             self.best_score = current