diff --git a/Misc/NEWS.d/next/Library/2020-05-05-08-12-51.bpo-40559.112wwa.rst b/Misc/NEWS.d/next/Library/2020-05-05-08-12-51.bpo-40559.112wwa.rst
new file mode 100644
index 00000000000000..15846351f25bbe
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-05-05-08-12-51.bpo-40559.112wwa.rst
@@ -0,0 +1 @@
+Fix possible memory leak in the C implementation of :class:`asyncio.Task`.
\ No newline at end of file
diff --git a/Modules/_asynciomodule.c b/Modules/_asynciomodule.c
index a03a63119bab3d..cc211a8895a8e8 100644
--- a/Modules/_asynciomodule.c
+++ b/Modules/_asynciomodule.c
@@ -2638,6 +2638,10 @@ task_step_impl(TaskObj *task, PyObject *exc)
     coro = task->task_coro;
     if (coro == NULL) {
         PyErr_SetString(PyExc_RuntimeError, "uninitialized Task object");
+        if (clear_exc) {
+            /* We created 'exc' during this call */
+            Py_DECREF(exc);
+        }
         return NULL;
     }