diff --git a/pytorch_lightning/trainer/connectors/checkpoint_connector.py b/pytorch_lightning/trainer/connectors/checkpoint_connector.py
index df6e8b8213c36..7ebd84a428de7 100644
--- a/pytorch_lightning/trainer/connectors/checkpoint_connector.py
+++ b/pytorch_lightning/trainer/connectors/checkpoint_connector.py
@@ -33,6 +33,7 @@
 from pytorch_lightning.utilities.cloud_io import load as pl_load
 from pytorch_lightning.utilities.upgrade_checkpoint import KEYS_MAPPING as DEPRECATED_CHECKPOINT_KEYS
 from pytorch_lightning.accelerators.base_backend import Accelerator
+from pytorch_lightning.utilities.exceptions import MisconfigurationException
 
 try:
     from apex import amp
@@ -145,6 +146,14 @@ def restore_training_state(self, checkpoint):
         self.trainer.global_step = checkpoint['global_step']
         self.trainer.current_epoch = checkpoint['epoch']
 
+        # crash if max_epochs is lower than the current epoch from the checkpoint
+        if self.trainer.current_epoch > self.trainer.max_epochs:
+            m = f"""
+            you restored a checkpoint with current_epoch={self.trainer.current_epoch}
+            but the Trainer(max_epochs={self.trainer.max_epochs})
+            """
+            raise MisconfigurationException(m)
+
         # Division deals with global step stepping once per accumulated batch
         # Inequality deals with different global step for odd vs even num_training_batches
         n_accum = 1 if self.trainer.accumulate_grad_batches is None else self.trainer.accumulate_grad_batches
diff --git a/tests/callbacks/test_early_stopping.py b/tests/callbacks/test_early_stopping.py
index d681d9cb894d8..d08a4f6fe35ea 100644
--- a/tests/callbacks/test_early_stopping.py
+++ b/tests/callbacks/test_early_stopping.py
@@ -9,6 +9,7 @@
 from pytorch_lightning import Trainer
 from pytorch_lightning.callbacks import EarlyStopping, ModelCheckpoint
 from tests.base import EvalModelTemplate
+from pytorch_lightning.utilities.exceptions import MisconfigurationException
 
 
 class EarlyStoppingTestRestore(EarlyStopping):
@@ -63,7 +64,9 @@ def test_resume_early_stopping_from_checkpoint(tmpdir):
         resume_from_checkpoint=checkpoint_filepath,
         early_stop_callback=early_stop_callback,
     )
-    new_trainer.fit(model)
+
+    with pytest.raises(MisconfigurationException, match=r'.*you restored a checkpoint with current_epoch*'):
+        new_trainer.fit(model)
 
 
 def test_early_stopping_no_extraneous_invocations(tmpdir):