diff --git a/pytorch_lightning/trainer/training_io.py b/pytorch_lightning/trainer/training_io.py
index 47448132df28a..09a65af0485de 100644
--- a/pytorch_lightning/trainer/training_io.py
+++ b/pytorch_lightning/trainer/training_io.py
@@ -281,6 +281,10 @@ def restore(self, checkpoint_path: str, on_gpu: bool):
         if on_gpu:
             model.cuda(self.root_gpu)
 
+        # restore amp scaling
+        if self.use_amp and self.use_native_amp and 'native_amp_scaling_state' in checkpoint:
+            self.scaler.load_state_dict(checkpoint['native_amp_scaling_state'])
+
         # load training state (affects trainer only)
         self.restore_training_state(checkpoint)
 
@@ -316,6 +320,10 @@ def dump_checkpoint(self):
 
         checkpoint['state_dict'] = model.state_dict()
 
+        # restore native amp scaling
+        if self.use_amp and self.use_native_amp and 'native_amp_scaling_state' in checkpoint:
+            checkpoint['native_amp_scaling_state'] = self.scaler.state_dict
+
         if hasattr(model, "hparams"):
             is_namespace = isinstance(model.hparams, Namespace)
             checkpoint['hparams'] = vars(model.hparams) if is_namespace else model.hparams
@@ -441,6 +449,10 @@ def hpc_load(self, folderpath, on_gpu):
         # load the state_dict on the model automatically
         model.load_state_dict(checkpoint['state_dict'])
 
+        # restore amp scaling
+        if self.use_amp and self.use_native_amp and 'native_amp_scaling_state' in checkpoint:
+            self.scaler.load_state_dict(checkpoint['native_amp_scaling_state'])
+
         if self.root_gpu is not None:
             model.cuda(self.root_gpu)