diff --git a/tensorflow/python/keras/layers/preprocessing/normalization.py b/tensorflow/python/keras/layers/preprocessing/normalization.py
index 07f8d40ec24..4b75def0247 100644
--- a/tensorflow/python/keras/layers/preprocessing/normalization.py
+++ b/tensorflow/python/keras/layers/preprocessing/normalization.py
@@ -156,7 +156,8 @@ class Normalization(base_preprocessing_layer.CombinerPreprocessingLayer):
     # broadcasts the data correctly.
     mean = array_ops.reshape(self.mean, self._broadcast_shape)
     variance = array_ops.reshape(self.variance, self._broadcast_shape)
-    return (inputs - mean) / math_ops.sqrt(variance)
+    return ((inputs - mean) /
+            math_ops.maximum(math_ops.sqrt(variance), K.epsilon()))
 
   def compute_output_shape(self, input_shape):
     return input_shape
diff --git a/tensorflow/python/keras/layers/preprocessing/normalization_test.py b/tensorflow/python/keras/layers/preprocessing/normalization_test.py
index f97b8db50ec..69eafc54adc 100644
--- a/tensorflow/python/keras/layers/preprocessing/normalization_test.py
+++ b/tensorflow/python/keras/layers/preprocessing/normalization_test.py
@@ -97,6 +97,16 @@ def _get_layer_computation_test_cases():
               np.float32),
       "testcase_name":
           "3d_multiple_axis"
+  }, {
+      "adapt_data":
+          np.zeros((3, 4)),
+      "axis": -1,
+      "test_data":
+          np.zeros((3, 4)),
+      "expected":
+          np.zeros((3, 4)),
+      "testcase_name":
+          "zero_variance"
   })
 
   crossed_test_cases = []