diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index 7ecec963848..8b05434f273 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -465,9 +465,12 @@ async def wait_for(fut, timeout, *, loop=None):
         try:
             await waiter
         except exceptions.CancelledError:
-            fut.remove_done_callback(cb)
-            fut.cancel()
-            raise
+            if fut.done():
+                return fut.result()
+            else:
+                fut.remove_done_callback(cb)
+                fut.cancel()
+                raise
 
         if fut.done():
             return fut.result()
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index 511961c3200..74fc1e4a421 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -1120,6 +1120,22 @@ class BaseTaskTests:
         res = loop.run_until_complete(task)
         self.assertEqual(res, "ok")
 
+    def test_wait_for_cancellation_race_condition(self):
+        def gen():
+            yield 0.1
+            yield 0.1
+            yield 0.1
+            yield 0.1
+
+        loop = self.new_test_loop(gen)
+
+        fut = self.new_future(loop)
+        loop.call_later(0.1, fut.set_result, "ok")
+        task = loop.create_task(asyncio.wait_for(fut, timeout=1))
+        loop.call_later(0.1, task.cancel)
+        res = loop.run_until_complete(task)
+        self.assertEqual(res, "ok")
+
     def test_wait_for_waits_for_task_cancellation(self):
         loop = asyncio.new_event_loop()
         self.addCleanup(loop.close)
diff --git a/Misc/NEWS.d/next/Library/2020-08-15-15-21-40.bpo-37658.f9nivB.rst b/Misc/NEWS.d/next/Library/2020-08-15-15-21-40.bpo-37658.f9nivB.rst
new file mode 100644
index 00000000000..694fbbbf346
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-08-15-15-21-40.bpo-37658.f9nivB.rst
@@ -0,0 +1,2 @@
+:meth:`asyncio.wait_for` now properly handles races between cancellation of
+itself and the completion of the wrapped awaitable.