diff --git a/tests/python/mkl/test_mkldnn.py b/tests/python/mkl/test_mkldnn.py
index e5490096f60f..c6c0a0832f1f 100644
--- a/tests/python/mkl/test_mkldnn.py
+++ b/tests/python/mkl/test_mkldnn.py
@@ -383,6 +383,21 @@ def check_fullyconnected_training(stype):
     for stype in stypes:
         check_fullyconnected_training(stype)
 
+def test_softmax_with_large_inputs():
+    def softmax_forward(input_data, true_output):
+        data = mx.sym.Variable('data')
+        out1 = data.softmax(axis=1)
+        exec1 = out1.bind(mx.cpu(), args={'data': input_data})
+        exec1.forward()[0].wait_to_read()
+        ndarr = exec1.outputs[0][0][0][0]
+        nparr = ndarr.asnumpy()
+        assert_almost_equal(nparr, true_output, rtol=1e-5, atol=1e-5)
+
+    softmax_forward(mx.nd.array([[[[-1e30,-1e30]]]]), np.array([1.0,1.0]))
+    softmax_forward(mx.nd.array([[[[1e30,1e30]]]]), np.array([1.0,1.0]))
+    softmax_forward(mx.nd.array([[[[-3.4e38,-3.4e38]]]]), np.array([1.0,1.0]))
+    softmax_forward(mx.nd.array([[[[3.4e38,3.4e38]]]]), np.array([1.0,1.0]))
+
 @with_seed()
 def test_non_mkldnn_fcomputeex():
     # test special case where MKLDNN formatted NDArray feeds into non-mkldnn fcomputeex operator
diff --git a/tests/python/unittest/test_operator.py b/tests/python/unittest/test_operator.py
index 1bf9ca0237ab..19b90b09ceb5 100644
--- a/tests/python/unittest/test_operator.py
+++ b/tests/python/unittest/test_operator.py
@@ -4449,6 +4449,20 @@ def test_log_softmax():
             check_symbolic_forward(sym, [data], [np.log(np_softmax(data, axis=axis)+1e-20)])
             check_numeric_gradient(sym, [data], rtol=0.05, atol=1e-3)
 
+def test_softmax_with_large_inputs():
+    def softmax_forward(input_data, true_output):
+        data = mx.sym.Variable('data')
+        out1 = data.softmax(axis=1)
+        exec1 = out1.bind(default_context(), args={'data': input_data})
+        exec1.forward()[0].wait_to_read()
+        ndarr = exec1.outputs[0][0][0][0]
+        nparr = ndarr.asnumpy()
+        assert_almost_equal(nparr, true_output, rtol=1e-5, atol=1e-5)
+
+    softmax_forward(mx.nd.array([[[[-1e30,-1e30]]]]), np.array([1.0,1.0]))
+    softmax_forward(mx.nd.array([[[[1e30,1e30]]]]), np.array([1.0,1.0]))
+    softmax_forward(mx.nd.array([[[[-3.4e38,-3.4e38]]]]), np.array([1.0,1.0]))
+    softmax_forward(mx.nd.array([[[[3.4e38,3.4e38]]]]), np.array([1.0,1.0]))
 
 @with_seed()
 def test_pick():