diff --git a/python/mxnet/contrib/onnx/mx2onnx/_op_translations.py b/python/mxnet/contrib/onnx/mx2onnx/_op_translations.py
index 15624b6c3a22..3baf10a10d39 100644
--- a/python/mxnet/contrib/onnx/mx2onnx/_op_translations.py
+++ b/python/mxnet/contrib/onnx/mx2onnx/_op_translations.py
@@ -810,7 +810,7 @@ def convert_l2normalization(node, **kwargs):
     mode = attrs.get("mode", "instance")
 
     if mode != "channel":
-        raise AttributeError("ONNX currently supports channel mode only")
+        raise AttributeError("L2Normalization: ONNX currently supports channel mode only")
 
     l2norm_node = onnx.helper.make_node(
         "LpNormalization",
@@ -1302,7 +1302,7 @@ def convert_reshape(node, **kwargs):
 
     for val in output_shape_list:
         if val in not_supported_shape:
-            raise AttributeError("Shape value not supported in ONNX", val)
+            raise AttributeError("Reshape: Shape value not supported in ONNX", val)
 
     reshape_node = onnx.helper.make_node(
         "Reshape",
@@ -1428,7 +1428,7 @@ def convert_squeeze(node, **kwargs):
 
     axis = attrs.get("axis", None)
     if not axis:
-        raise AttributeError("Missing axis attribute: ONNX currently requires axis to "
+        raise AttributeError("Squeeze: Missing axis attribute: ONNX currently requires axis to "
                              "be specified for squeeze operator")
     axis = convert_string_to_list(axis)
 
@@ -1666,3 +1666,26 @@ def convert_size(node, **kwargs):
     and return the created node.
     """
     return create_basic_op_node('Size', node, kwargs)
+
+
+@mx_op.register("log_softmax")
+def convert_logsoftmax(node, **kwargs):
+    """Map MXNet's log_softmax operator attributes to onnx's LogSoftMax operator
+    and return the created node.
+    """
+    name, input_nodes, attrs = get_inputs(node, kwargs)
+
+    # Converting to int
+    axis = int(attrs.get("axis", -1))
+    temp = attrs.get("temperature", 'None')
+    if temp != 'None':
+        raise AttributeError("LogSoftMax: ONNX supports only temperature=None")
+
+    node = onnx.helper.make_node(
+        'LogSoftmax',
+        input_nodes,
+        [name],
+        axis=axis,
+        name=name
+    )
+    return [node]
diff --git a/python/mxnet/contrib/onnx/mx2onnx/export_onnx.py b/python/mxnet/contrib/onnx/mx2onnx/export_onnx.py
index 84db5decd503..d0d4501d89f4 100644
--- a/python/mxnet/contrib/onnx/mx2onnx/export_onnx.py
+++ b/python/mxnet/contrib/onnx/mx2onnx/export_onnx.py
@@ -146,7 +146,7 @@ def get_outputs(sym, params, in_shape, in_label):
             if name.endswith('_output'):
                 out_names.append(name[:-len('_output')])
             else:
-                logging.warning("output '%s' does not end with '_output'", name)
+                logging.info("output '%s' does not end with '_output'", name)
                 out_names.append(name)
 
         assert len(out_shapes) == len(out_names)
diff --git a/tests/python-pytest/onnx/backend_rep.py b/tests/python-pytest/onnx/backend_rep.py
index bcb99ab025cc..be6bc88d9d70 100644
--- a/tests/python-pytest/onnx/backend_rep.py
+++ b/tests/python-pytest/onnx/backend_rep.py
@@ -82,8 +82,10 @@ def run(self, inputs, **kwargs):
         args = dict(zip(data_names, data_forward))
         exe = self.symbol.bind(ctx, args=args, aux_states=self.aux_params)
         exe.forward(is_train=False)
-        result = exe.outputs[0].asnumpy()
-        return [result]
+        result = []
+        for output in exe.outputs:
+            result.append(output.asnumpy())
+        return result
 
 
 # GluonBackendRep object will be returned by GluonBackend's prepare method which is used to
@@ -124,7 +126,12 @@ def run(self, inputs, **kwargs):
         net_inputs = [nd.array(input_data, ctx=ctx) for input_data in inputs]
         net_outputs = self.net(*net_inputs)
         results = []
-        results.extend([o for o in net_outputs.asnumpy()])
-        result = np.array(results)
+        if isinstance(net_outputs, list):
+            for output in net_outputs:
+                results.append(output.asnumpy())
+            result = results
+        else:
+            results.extend([o for o in net_outputs.asnumpy()])
+            result = [np.array(results)]
 
-        return [result]
+        return result
diff --git a/tests/python-pytest/onnx/test_cases.py b/tests/python-pytest/onnx/test_cases.py
index 1001836cc408..92e80e056701 100644
--- a/tests/python-pytest/onnx/test_cases.py
+++ b/tests/python-pytest/onnx/test_cases.py
@@ -49,7 +49,7 @@
              'test_argmin',
              'test_min',
              # pytorch operator tests
-             'test_operator_exp',
+             'test_exp_',
              'test_operator_maxpool',
              'test_operator_params',
              'test_operator_permute2',
@@ -60,21 +60,28 @@
              'test_asin',
              'test_atan',
              'test_squeeze',
-             'test_matmul_3d',
-             'test_matmul_4d',
+             'test_matmul',
              'test_depthtospace',
              'test_hardsigmoid',
              'test_instancenorm',
              'test_shape',
              'test_cast',
              'test_clip',
-             'test_size'
+             'test_size',
+             'test_dropout',
+             'test_unsqueeze',
+             'test_log_',
+             'test_flatten_default_axis',
+             'test_leakyrelu',
+             'test_selu_default',
+             'test_elu',
+             'test_max_',
+             'test_softplus'
              ],
-    'import': ['test_unsqueeze',
+    'import': ['test_gather',
                'test_global_lppooling',
                'test_softsign',
                'test_reduce_',
-               'test_softplus',
                'test_mean',
                'test_averagepool_1d',
                'test_averagepool_2d_pads_count_include_pad',
@@ -84,18 +91,16 @@
                'test_averagepool_3d',
                'test_LpPool_',
                'test_split_equal'
-               'test_random_',
                ],
     'export': ['test_random_uniform',
                'test_random_normal',
                'test_reduce_min',
                'test_reduce_max',
-               'test_squeeze',
                'test_reduce_mean',
                'test_reduce_prod',
                'test_reduce_sum_d',
                'test_reduce_sum_keepdims_random',
-               'test_max_',
+               'test_lrn'
                ]
 }
 
@@ -104,17 +109,12 @@
              'test_BatchNorm',
              'test_ConstantPad2d'
              'test_Conv2d',
-             'test_ELU',
-             'test_LeakyReLU',
              'test_MaxPool',
              'test_PReLU',
-             'test_ReLU',
-             'test_selu_default',
-             'test_Sigmoid',
              'test_Softmax',
              'test_softmax_functional',
              'test_softmax_lastdim',
-             'test_Tanh']
+             ]
 }
 
 STANDARD_MODEL = {