diff --git a/python/gtsam/tests/test_Robust.py b/python/gtsam/tests/test_Robust.py
new file mode 100644
index 000000000..c2ab9d4a4
--- /dev/null
+++ b/python/gtsam/tests/test_Robust.py
@@ -0,0 +1,43 @@
+"""
+GTSAM Copyright 2010-2019, Georgia Tech Research Corporation,
+Atlanta, Georgia 30332-0415
+All Rights Reserved
+
+See LICENSE for the license information
+
+Simple unit test for custom robust noise model.
+Author: Fan Jiang
+"""
+import unittest
+
+import gtsam
+import numpy as np
+from gtsam.utils.test_case import GtsamTestCase
+
+
+class TestRobust(GtsamTestCase):
+
+    def test_RobustLossAndWeight(self):
+        k = 10.0
+
+        def custom_weight(e):
+            abs_e = abs(e)
+            return 1.0 if abs_e <= k else k / abs_e
+
+        def custom_loss(e):
+            abs_e = abs(e)
+            return abs_e * abs_e / 2.0 if abs_e <= k else k * abs_e - k * k / 2.0
+
+        custom_robust = gtsam.noiseModel.Robust.Create(
+            gtsam.noiseModel.mEstimator.Custom(custom_weight, custom_loss,
+                                               gtsam.noiseModel.mEstimator.Base.ReweightScheme.Scalar,
+                                               "huber"),
+            gtsam.noiseModel.Isotropic.Sigma(1, 2.0))
+        f = gtsam.PriorFactorDouble(0, 1.0, custom_robust)
+        v = gtsam.Values()
+        v.insert(0, 0.0)
+
+        self.assertAlmostEquals(f.error(v), 0.125)
+
+if __name__ == "__main__":
+    unittest.main()