diff --git a/tests/python/unittest/test_higher_order_grad.py b/tests/python/unittest/test_higher_order_grad.py
new file mode 100644
index 000000000000..92c78d15318d
--- /dev/null
+++ b/tests/python/unittest/test_higher_order_grad.py
@@ -0,0 +1,80 @@
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+
+import math
+
+from mxnet import nd, autograd
+from mxnet.test_utils import assert_almost_equal, random_arrays
+from common import with_seed
+
+
+@with_seed()
+def test_log():
+    def log(x):
+        return nd.log(x)
+
+    def grad_grad_op(x):
+        return -1/(x**2)
+
+    arrays = random_arrays((2, 2), (2, 3), (4, 5, 2), (3, 1, 4, 5))
+
+    for array in arrays:
+        check_second_order_unary(array, log, grad_grad_op)
+
+
+@with_seed()
+def test_log2():
+    def log2(x):
+        return nd.log2(x)
+
+    def grad_grad_op(x):
+        return -1/((x**2) * math.log(2))
+
+    arrays = random_arrays((2, 2), (2, 3), (4, 5, 2), (3, 1, 4, 5))
+
+    for array in arrays:
+        check_second_order_unary(array, log2, grad_grad_op)
+
+
+@with_seed()
+def test_log10():
+    def log10(x):
+        return nd.log10(x)
+
+    def grad_grad_op(x):
+        return -1/((x**2) * math.log(10))
+
+    arrays = random_arrays((2, 2), (2, 3), (4, 5, 2), (3, 1, 4, 5))
+
+    for array in arrays:
+        check_second_order_unary(array, log10, grad_grad_op)
+
+
+def check_second_order_unary(x, op, grad_grad_op):
+    x = nd.array(x)
+    expect_grad_grad = grad_grad_op(x)
+    x.attach_grad()
+    with autograd.record():
+        y = op(x)
+        y_grad = autograd.grad(y, x, create_graph=True, retain_graph=True)[0]
+    y_grad.backward()
+    assert_almost_equal(expect_grad_grad.asnumpy(), x.grad.asnumpy())
+
+
+if __name__ == '__main__':
+    import nose
+    nose.runmodule()