diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index 575d205404a..52fef181cec 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -334,6 +334,15 @@ def wait_for(fut, timeout, *, loop=None):
     if timeout is None:
         return (yield from fut)
 
+    if timeout <= 0:
+        fut = ensure_future(fut, loop=loop)
+
+        if fut.done():
+            return fut.result()
+
+        fut.cancel()
+        raise futures.TimeoutError()
+
     waiter = loop.create_future()
     timeout_handle = loop.call_later(timeout, _release_waiter, waiter)
     cb = functools.partial(_release_waiter, waiter)
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index 36082ec7c6a..7ff56b560b6 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -661,6 +661,76 @@ class BaseTaskTests:
         t.cancel()
         self.assertRaises(asyncio.CancelledError, loop.run_until_complete, t)
 
+    def test_wait_for_timeout_less_then_0_or_0_future_done(self):
+        def gen():
+            when = yield
+            self.assertAlmostEqual(0, when)
+
+        loop = self.new_test_loop(gen)
+
+        fut = self.new_future(loop)
+        fut.set_result('done')
+
+        ret = loop.run_until_complete(asyncio.wait_for(fut, 0, loop=loop))
+
+        self.assertEqual(ret, 'done')
+        self.assertTrue(fut.done())
+        self.assertAlmostEqual(0, loop.time())
+
+    def test_wait_for_timeout_less_then_0_or_0_coroutine_do_not_started(self):
+        def gen():
+            when = yield
+            self.assertAlmostEqual(0, when)
+
+        loop = self.new_test_loop(gen)
+
+        foo_started = False
+
+        @asyncio.coroutine
+        def foo():
+            nonlocal foo_started
+            foo_started = True
+
+        with self.assertRaises(asyncio.TimeoutError):
+            loop.run_until_complete(asyncio.wait_for(foo(), 0, loop=loop))
+
+        self.assertAlmostEqual(0, loop.time())
+        self.assertEqual(foo_started, False)
+
+    def test_wait_for_timeout_less_then_0_or_0(self):
+        def gen():
+            when = yield
+            self.assertAlmostEqual(0.2, when)
+            when = yield 0
+            self.assertAlmostEqual(0, when)
+
+        for timeout in [0, -1]:
+            with self.subTest(timeout=timeout):
+                loop = self.new_test_loop(gen)
+
+                foo_running = None
+
+                @asyncio.coroutine
+                def foo():
+                    nonlocal foo_running
+                    foo_running = True
+                    try:
+                        yield from asyncio.sleep(0.2, loop=loop)
+                    finally:
+                        foo_running = False
+                    return 'done'
+
+                fut = self.new_task(loop, foo())
+
+                with self.assertRaises(asyncio.TimeoutError):
+                    loop.run_until_complete(asyncio.wait_for(
+                        fut, timeout, loop=loop))
+                self.assertTrue(fut.done())
+                # it should have been cancelled due to the timeout
+                self.assertTrue(fut.cancelled())
+                self.assertAlmostEqual(0, loop.time())
+                self.assertEqual(foo_running, False)
+
     def test_wait_for(self):
 
         def gen():
diff --git a/Misc/NEWS.d/next/Library/2017-09-22-23-48-49.bpo-31556.9J0u5H.rst b/Misc/NEWS.d/next/Library/2017-09-22-23-48-49.bpo-31556.9J0u5H.rst
new file mode 100644
index 00000000000..2e6b0284696
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2017-09-22-23-48-49.bpo-31556.9J0u5H.rst
@@ -0,0 +1 @@
+Cancel asyncio.wait_for future faster if timeout <= 0