diff --git a/Lib/asyncio/locks.py b/Lib/asyncio/locks.py
index 4fef64e3921e17..7b81c25b2d9e76 100644
--- a/Lib/asyncio/locks.py
+++ b/Lib/asyncio/locks.py
@@ -6,6 +6,7 @@
 
 from . import exceptions
 from . import mixins
+from . import tasks
 
 
 class _ContextManagerMixin:
@@ -350,6 +351,7 @@ def __init__(self, value=1, *, loop=mixins._marker):
             raise ValueError("Semaphore initial value must be >= 0")
         self._value = value
         self._waiters = collections.deque()
+        self._wakeup_scheduled = False
 
     def __repr__(self):
         res = super().__repr__()
@@ -363,6 +365,7 @@ def _wake_up_next(self):
             waiter = self._waiters.popleft()
             if not waiter.done():
                 waiter.set_result(None)
+                self._wakeup_scheduled = True
                 return
 
     def locked(self):
@@ -378,16 +381,17 @@ async def acquire(self):
         called release() to make it larger than 0, and then return
         True.
         """
-        while self._value <= 0:
+        # _wakeup_scheduled is set if *another* task is scheduled to wakeup
+        # but its acquire() is not resumed yet
+        while self._wakeup_scheduled or self._value <= 0:
             fut = self._get_loop().create_future()
             self._waiters.append(fut)
             try:
                 await fut
-            except:
-                # See the similar code in Queue.get.
-                fut.cancel()
-                if self._value > 0 and not fut.cancelled():
-                    self._wake_up_next()
+                # reset _wakeup_scheduled *after* waiting for a future
+                self._wakeup_scheduled = False
+            except exceptions.CancelledError:
+                self._wake_up_next()
                 raise
         self._value -= 1
         return True
diff --git a/Lib/test/test_asyncio/test_locks.py b/Lib/test/test_asyncio/test_locks.py
index e2cd2ba0365fda..c5e3fdcbc955a5 100644
--- a/Lib/test/test_asyncio/test_locks.py
+++ b/Lib/test/test_asyncio/test_locks.py
@@ -933,6 +933,32 @@ async def test_release_no_waiters(self):
         sem.release()
         self.assertFalse(sem.locked())
 
+    async def test_acquire_fifo_order(self):
+        sem = asyncio.Semaphore(1)
+        result = []
+
+        async def coro(tag):
+            await sem.acquire()
+            result.append(f'{tag}_1')
+            await asyncio.sleep(0.01)
+            sem.release()
+
+            await sem.acquire()
+            result.append(f'{tag}_2')
+            await asyncio.sleep(0.01)
+            sem.release()
+
+        t1 = asyncio.create_task(coro('c1'))
+        t2 = asyncio.create_task(coro('c2'))
+        t3 = asyncio.create_task(coro('c3'))
+
+        await asyncio.gather(t1, t2, t3)
+
+        self.assertEqual(
+            ['c1_1', 'c2_1', 'c3_1', 'c1_2', 'c2_2', 'c3_2'],
+            result
+        )
+
 
 if __name__ == '__main__':
     unittest.main()
diff --git a/Misc/NEWS.d/next/Library/2022-03-15-18-32-12.bpo-45997.4n2aVU.rst b/Misc/NEWS.d/next/Library/2022-03-15-18-32-12.bpo-45997.4n2aVU.rst
new file mode 100644
index 00000000000000..40d8504e5a946b
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2022-03-15-18-32-12.bpo-45997.4n2aVU.rst
@@ -0,0 +1 @@
+Fix :class:`asyncio.Semaphore` re-aquiring FIFO order.