diff --git a/lms/djangoapps/courseware/module_render.py b/lms/djangoapps/courseware/module_render.py
index 4e1e114d8e..7100e52a8e 100644
--- a/lms/djangoapps/courseware/module_render.py
+++ b/lms/djangoapps/courseware/module_render.py
@@ -577,16 +577,17 @@ def get_module_system_for_user(
         """
         Submit a grade for the block.
         """
-        grades_signals.SCORE_PUBLISHED.send(
-            sender=None,
-            block=block,
-            user=user,
-            raw_earned=event['value'],
-            raw_possible=event['max_value'],
-            only_if_higher=event.get('only_if_higher'),
-            score_deleted=event.get('score_deleted'),
-            grader_response=event.get('grader_response')
-        )
+        if not user.is_anonymous():
+            grades_signals.SCORE_PUBLISHED.send(
+                sender=None,
+                block=block,
+                user=user,
+                raw_earned=event['value'],
+                raw_possible=event['max_value'],
+                only_if_higher=event.get('only_if_higher'),
+                score_deleted=event.get('score_deleted'),
+                grader_response=event.get('grader_response')
+            )
 
     def handle_deprecated_progress_event(block, event):
         """
diff --git a/lms/djangoapps/courseware/tests/test_module_render.py b/lms/djangoapps/courseware/tests/test_module_render.py
index 65f08d38d4..7bd8c57119 100644
--- a/lms/djangoapps/courseware/tests/test_module_render.py
+++ b/lms/djangoapps/courseware/tests/test_module_render.py
@@ -906,6 +906,26 @@ class TestHandleXBlockCallback(SharedModuleStoreTestCase, LoginEnrollmentTestCas
         with self.assertRaises(BlockCompletion.DoesNotExist):
             BlockCompletion.objects.get(block_key=block.scope_ids.usage_id)
 
+    @XBlock.register_temp_plugin(GradedStatelessXBlock, identifier='stateless_scorer')
+    @patch('lms.djangoapps.courseware.module_render.grades_signals.SCORE_PUBLISHED.send')
+    def test_anonymous_user_not_be_graded(self, mock_score_signal):
+        course = CourseFactory.create()
+        descriptor_kwargs = {
+            'category': 'problem',
+        }
+        request = self.request_factory.get('/')
+        request.user = AnonymousUser()
+        descriptor = ItemFactory.create(**descriptor_kwargs)
+
+        render.handle_xblock_callback(
+            request,
+            text_type(course.id),
+            quote_slashes(text_type(descriptor.location)),
+            'xmodule_handler',
+            'problem_check',
+        )
+        self.assertFalse(mock_score_signal.called)
+
 
 @ddt.ddt
 @patch.dict('django.conf.settings.FEATURES', {'ENABLE_XBLOCK_VIEW_ENDPOINT': True})