diff --git a/tensorflow_addons/layers/normalizations_test.py b/tensorflow_addons/layers/normalizations_test.py
index 8c40a9a0af..b6aca121ef 100644
--- a/tensorflow_addons/layers/normalizations_test.py
+++ b/tensorflow_addons/layers/normalizations_test.py
@@ -139,6 +139,7 @@ def _test_specific_layer(self, inputs, axis, groups, center, scale):
 
     def _create_and_fit_Sequential_model(self, layer, shape):
         # Helperfunction for quick evaluation
+        np.random.seed(0x2020)
         model = tf.keras.models.Sequential()
         model.add(layer)
         model.add(tf.keras.layers.Dense(32))
@@ -233,6 +234,7 @@ def test_regularizations(self):
     def test_groupnorm_conv(self):
         # Check if Axis is working for CONV nets
         # Testing for 1 == LayerNorm, 5 == GroupNorm, -1 == InstanceNorm
+        np.random.seed(0x2020)
         groups = [-1, 5, 1]
         for i in groups:
             model = tf.keras.models.Sequential()
@@ -246,6 +248,85 @@ def test_groupnorm_conv(self):
             model.fit(x=x, y=y, epochs=1)
             self.assertTrue(hasattr(model.layers[0], "gamma"))
 
+    def test_groupnorm_correctness_1d(self):
+        np.random.seed(0x2020)
+        model = tf.keras.models.Sequential()
+        norm = GroupNormalization(input_shape=(10,), groups=2)
+        model.add(norm)
+        model.compile(loss="mse", optimizer="rmsprop")
+
+        x = np.random.normal(loc=5.0, scale=10.0, size=(1000, 10))
+        model.fit(x, x, epochs=5, verbose=0)
+        out = model.predict(x)
+        out -= self.evaluate(norm.beta)
+        out /= self.evaluate(norm.gamma)
+
+        self.assertAllClose(out.mean(), 0.0, atol=1e-1)
+        self.assertAllClose(out.std(), 1.0, atol=1e-1)
+
+    def test_groupnorm_2d_different_groups(self):
+        np.random.seed(0x2020)
+        groups = [2, 1, 10]
+        for i in groups:
+            model = tf.keras.models.Sequential()
+            norm = GroupNormalization(axis=1, groups=i, input_shape=(10, 3))
+            model.add(norm)
+            # centered and variance are 5.0 and 10.0, respectively
+            model.compile(loss="mse", optimizer="rmsprop")
+            x = np.random.normal(loc=5.0, scale=10.0, size=(1000, 10, 3))
+            model.fit(x, x, epochs=5, verbose=0)
+            out = model.predict(x)
+            out -= np.reshape(self.evaluate(norm.beta), (1, 10, 1))
+            out /= np.reshape(self.evaluate(norm.gamma), (1, 10, 1))
+
+            self.assertAllClose(
+                out.mean(axis=(0, 1), dtype=np.float32), (0.0, 0.0, 0.0), atol=1e-1
+            )
+            self.assertAllClose(
+                out.std(axis=(0, 1), dtype=np.float32), (1.0, 1.0, 1.0), atol=1e-1
+            )
+
+    def test_groupnorm_convnet(self):
+        np.random.seed(0x2020)
+        model = tf.keras.models.Sequential()
+        norm = GroupNormalization(axis=1, input_shape=(3, 4, 4), groups=3)
+        model.add(norm)
+        model.compile(loss="mse", optimizer="sgd")
+
+        # centered = 5.0, variance  = 10.0
+        x = np.random.normal(loc=5.0, scale=10.0, size=(1000, 3, 4, 4))
+        model.fit(x, x, epochs=4, verbose=0)
+        out = model.predict(x)
+        out -= np.reshape(self.evaluate(norm.beta), (1, 3, 1, 1))
+        out /= np.reshape(self.evaluate(norm.gamma), (1, 3, 1, 1))
+
+        self.assertAllClose(
+            np.mean(out, axis=(0, 2, 3), dtype=np.float32), (0.0, 0.0, 0.0), atol=1e-1
+        )
+        self.assertAllClose(
+            np.std(out, axis=(0, 2, 3), dtype=np.float32), (1.0, 1.0, 1.0), atol=1e-1
+        )
+
+    def test_groupnorm_convnet_no_center_no_scale(self):
+        np.random.seed(0x2020)
+        model = tf.keras.models.Sequential()
+        norm = GroupNormalization(
+            axis=-1, groups=2, center=False, scale=False, input_shape=(3, 4, 4)
+        )
+        model.add(norm)
+        model.compile(loss="mse", optimizer="sgd")
+        # centered and variance are  5.0 and 10.0, respectively
+        x = np.random.normal(loc=5.0, scale=10.0, size=(1000, 3, 4, 4))
+        model.fit(x, x, epochs=4, verbose=0)
+        out = model.predict(x)
+
+        self.assertAllClose(
+            np.mean(out, axis=(0, 2, 3), dtype=np.float32), (0.0, 0.0, 0.0), atol=1e-1
+        )
+        self.assertAllClose(
+            np.std(out, axis=(0, 2, 3), dtype=np.float32), (1.0, 1.0, 1.0), atol=1e-1
+        )
+
 
 if __name__ == "__main__":
     tf.test.main()