diff --git a/Lib/test/test_asyncgen.py b/Lib/test/test_asyncgen.py
index 23eb6a411cd..58d8aee19ad 100644
--- a/Lib/test/test_asyncgen.py
+++ b/Lib/test/test_asyncgen.py
@@ -735,6 +735,33 @@ class AsyncGenAsyncioTest(unittest.TestCase):
         self.loop.run_until_complete(run())
         self.assertEqual(DONE, 10)
 
+    def test_async_gen_asyncio_aclose_12(self):
+        DONE = 0
+
+        async def target():
+            await asyncio.sleep(0.01)
+            1 / 0
+
+        async def foo():
+            nonlocal DONE
+            task = asyncio.create_task(target())
+            try:
+                yield 1
+            finally:
+                try:
+                    await task
+                except ZeroDivisionError:
+                    DONE = 1
+
+        async def run():
+            gen = foo()
+            it = gen.__aiter__()
+            await it.__anext__()
+            await gen.aclose()
+
+        self.loop.run_until_complete(run())
+        self.assertEqual(DONE, 1)
+
     def test_async_gen_asyncio_asend_01(self):
         DONE = 0
 
diff --git a/Misc/NEWS.d/next/Core and Builtins/2019-07-13-18-01-13.bpo-35409.ozbcsR.rst b/Misc/NEWS.d/next/Core and Builtins/2019-07-13-18-01-13.bpo-35409.ozbcsR.rst
new file mode 100644
index 00000000000..0f35a91ec74
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2019-07-13-18-01-13.bpo-35409.ozbcsR.rst	
@@ -0,0 +1,2 @@
+Ignore GeneratorExit exceptions when throwing an exception into the aclose
+coroutine of an asynchronous generator.
diff --git a/Objects/genobject.c b/Objects/genobject.c
index 6285219bb2d..5643553b708 100644
--- a/Objects/genobject.c
+++ b/Objects/genobject.c
@@ -1947,6 +1947,17 @@ async_gen_athrow_throw(PyAsyncGenAThrow *o, PyObject *args)
             PyErr_SetString(PyExc_RuntimeError, ASYNC_GEN_IGNORED_EXIT_MSG);
             return NULL;
         }
+        if (PyErr_ExceptionMatches(PyExc_StopAsyncIteration) ||
+            PyErr_ExceptionMatches(PyExc_GeneratorExit))
+        {
+            /* when aclose() is called we don't want to propagate
+               StopAsyncIteration or GeneratorExit; just raise
+               StopIteration, signalling that this 'aclose()' await
+               is done.
+            */
+            PyErr_Clear();
+            PyErr_SetNone(PyExc_StopIteration);
+        }
         return retval;
     }
 }