diff --git a/src/python/grpcio/grpc/aio/_call.py b/src/python/grpcio/grpc/aio/_call.py
index 24f2090651a..be8855d059b 100644
--- a/src/python/grpcio/grpc/aio/_call.py
+++ b/src/python/grpcio/grpc/aio/_call.py
@@ -420,6 +420,14 @@ class _StreamRequestMixin(Call):
             self._async_request_poller = self._loop.create_task(
                 self._consume_request_iterator(request_iterator)
             )
+            # Cancel the Task when the RPC is done.
+            # If the RPC fails immediately but this Task is still pending or running,
+            # these errors will occur:
+            # - Task was destroyed but it is pending!
+            # - aclose(): asynchronous generator is already running
+            self.add_done_callback(
+                lambda call: call._async_request_poller.cancel()
+            )
             self._request_style = _APIStyle.ASYNC_GENERATOR
         else:
             self._async_request_poller = None
diff --git a/src/python/grpcio_tests/tests_aio/unit/_test_server.py b/src/python/grpcio_tests/tests_aio/unit/_test_server.py
index 5d25272f300..849a14cca0a 100644
--- a/src/python/grpcio_tests/tests_aio/unit/_test_server.py
+++ b/src/python/grpcio_tests/tests_aio/unit/_test_server.py
@@ -120,6 +120,14 @@ class TestServiceServicer(test_pb2_grpc.TestServiceServicer):
             aggregated_payload_size=aggregate_size
         )
 
+    async def StreamingInputCallWithUnavailable(
+        self, unused_request_async_iterator, context
+    ):
+        self._append_to_log()
+        await context.abort(
+            grpc.StatusCode.UNAVAILABLE, "Service is unavailable"
+        )
+
     async def FullDuplexCall(self, request_async_iterator, context):
         self._append_to_log()
         await _maybe_echo_metadata(context)
@@ -151,7 +159,12 @@ def _create_extra_generic_handler(servicer: TestServiceServicer):
             servicer.UnaryCallWithSleep,
             request_deserializer=messages_pb2.SimpleRequest.FromString,
             response_serializer=messages_pb2.SimpleResponse.SerializeToString,
-        )
+        ),
+        "StreamingInputCallWithUnavailable": grpc.stream_unary_rpc_method_handler(
+            servicer.StreamingInputCallWithUnavailable,
+            request_deserializer=messages_pb2.StreamingInputCallRequest.FromString,
+            response_serializer=messages_pb2.StreamingInputCallResponse.SerializeToString,
+        ),
     }
     return grpc.method_handlers_generic_handler(
         "grpc.testing.TestService", rpc_method_handlers
diff --git a/src/python/grpcio_tests/tests_aio/unit/channel_test.py b/src/python/grpcio_tests/tests_aio/unit/channel_test.py
index 26ef006fa15..5dac1fbd587 100644
--- a/src/python/grpcio_tests/tests_aio/unit/channel_test.py
+++ b/src/python/grpcio_tests/tests_aio/unit/channel_test.py
@@ -30,6 +30,9 @@ from tests_aio.unit._test_server import start_test_server
 
 _UNARY_CALL_METHOD = "/grpc.testing.TestService/UnaryCall"
 _UNARY_CALL_METHOD_WITH_SLEEP = "/grpc.testing.TestService/UnaryCallWithSleep"
+_STREAMING_INPUT_CALL_METHOD_WITH_UNAVAILABLE = (
+    "/grpc.testing.TestService/StreamingInputCallWithUnavailable"
+)
 _STREAMING_OUTPUT_CALL_METHOD = "/grpc.testing.TestService/StreamingOutputCall"
 
 _INVOCATION_METADATA = (
@@ -198,6 +201,37 @@ class TestChannel(AioTestBase):
         self.assertEqual(await call.code(), grpc.StatusCode.OK)
         await channel.close()
 
+    async def test_stream_unary_unavailable_using_async_gen(self):
+        channel = aio.insecure_channel(self._server_target)
+        hi = channel.stream_unary(
+            _STREAMING_INPUT_CALL_METHOD_WITH_UNAVAILABLE,
+            request_serializer=messages_pb2.StreamingInputCallRequest.SerializeToString,
+            response_deserializer=messages_pb2.StreamingInputCallResponse.FromString,
+        )
+        # Prepares the request
+        payload = messages_pb2.Payload(body=b"\0" * _REQUEST_PAYLOAD_SIZE)
+        request = messages_pb2.StreamingInputCallRequest(payload=payload)
+
+        async def gen():
+            for _ in range(_NUM_STREAM_RESPONSES):
+                yield request
+
+        # Invokes the actual RPC
+        call: aio.StreamUnaryCall = hi(gen())
+
+        # Validates the responses
+        with self.assertRaises(aio.AioRpcError) as exception_context:
+            await call
+        self.assertEqual(
+            grpc.StatusCode.UNAVAILABLE,
+            exception_context.exception.code(),
+        )
+        self.assertTrue(call.done())
+        self.assertEqual(grpc.StatusCode.UNAVAILABLE, await call.code())
+
+        # Verify the async request poller task is done
+        self.assertTrue(call._async_request_poller.done())
+
     async def test_stream_stream_using_read_write(self):
         channel = aio.insecure_channel(self._server_target)
         stub = test_pb2_grpc.TestServiceStub(channel)