diff --git a/tempest/api/volume/admin/test_group_types.py b/tempest/api/volume/admin/test_group_types.py
index 8154682..406af27 100644
--- a/tempest/api/volume/admin/test_group_types.py
+++ b/tempest/api/volume/admin/test_group_types.py
@@ -71,3 +71,39 @@
             self.admin_group_types_client.list_group_types()['group_types'])
         group_ids = [it['id'] for it in group_list]
         self.assertNotIn(body['id'], group_ids)
+
+    @decorators.idempotent_id('3d5e5cec-72b4-4511-b135-7cc2b7a053ae')
+    def test_group_type_list_by_optional_params(self):
+        """Test list group type sort/public"""
+        type_a_name = "a_{}".format(data_utils.rand_name('group-type'))
+        type_b_name = "b_{}".format(data_utils.rand_name('group-type'))
+        self.create_group_type(name=type_a_name, **{'is_public': True})
+        self.create_group_type(name=type_b_name, **{'is_public': False})
+
+        group_list = (
+            self.admin_group_types_client.list_group_types(
+                sort="name:asc", is_public=None)['group_types'])
+        name_list = [it['name'] for it in group_list]
+        self.assertLess(
+            name_list.index(type_a_name), name_list.index(type_b_name))
+
+        group_list = (
+            self.admin_group_types_client.list_group_types(
+                sort="name:desc", is_public=None)['group_types'])
+        name_list = [it['name'] for it in group_list]
+        self.assertLess(name_list.index(type_b_name),
+                        name_list.index(type_a_name))
+
+        group_list = (
+            self.admin_group_types_client.list_group_types(
+                is_public=False)['group_types'])
+        name_list = [it['name'] for it in group_list]
+        self.assertNotIn(type_a_name, name_list)
+        self.assertIn(type_b_name, name_list)
+
+        group_list = (
+            self.admin_group_types_client.list_group_types(
+                is_public=True)['group_types'])
+        name_list = [it['name'] for it in group_list]
+        self.assertNotIn(type_b_name, name_list)
+        self.assertIn(type_a_name, name_list)