diff --git a/CHANGES/3406.feature b/CHANGES/3406.feature
new file mode 100644
index 00000000000..c6ce99a386a
--- /dev/null
+++ b/CHANGES/3406.feature
@@ -0,0 +1 @@
+Create a task per request handling.
diff --git a/aiohttp/web_protocol.py b/aiohttp/web_protocol.py
index a47919f6738..0919f86277d 100644
--- a/aiohttp/web_protocol.py
+++ b/aiohttp/web_protocol.py
@@ -400,7 +400,10 @@ async def start(self) -> None:
                 message, payload, self, writer, handler)
             try:
                 try:
-                    resp = await self._request_handler(request)
+                    # a new task is used for copy context vars (#3406)
+                    task = self._loop.create_task(
+                        self._request_handler(request))
+                    resp = await task
                 except HTTPException as exc:
                     resp = exc
                 except asyncio.CancelledError:
diff --git a/tests/test_web_protocol.py b/tests/test_web_protocol.py
index caaf91b7934..829d1ec4fae 100644
--- a/tests/test_web_protocol.py
+++ b/tests/test_web_protocol.py
@@ -237,7 +237,7 @@ async def test_simple(srv, buf) -> None:
     srv.data_received(
         b'GET / HTTP/1.1\r\n\r\n')
 
-    await asyncio.sleep(0)
+    await asyncio.sleep(0.05)
     assert buf.startswith(b'HTTP/1.1 200 OK\r\n')
 
 
@@ -450,7 +450,7 @@ async def handle_request(request):
         b'Content-Length: 50\r\n\r\n')
     await asyncio.sleep(0)
     assert not transport.close.called
-    await asyncio.sleep(0)
+    await asyncio.sleep(0.05)
     transport.close.assert_called_with()
 
 
@@ -465,7 +465,7 @@ async def handle_request(request):
     srv.connection_made(transport)
     request_handler.side_effect = handle_request
 
-    await asyncio.sleep(0)
+    await asyncio.sleep(0.05)
     assert not transport.close.called
 
     srv.data_received(
@@ -475,7 +475,7 @@ async def handle_request(request):
     await asyncio.sleep(0)
     assert not transport.close.called
 
-    await asyncio.sleep(0)
+    await asyncio.sleep(0.05)
     transport.close.assert_called_with()
 
 
@@ -490,7 +490,7 @@ async def test_handle_payload_access_error(
         b'some data'
     )
     # start request_handler task
-    await asyncio.sleep(0)
+    await asyncio.sleep(0.05)
 
     with pytest.raises(web.PayloadAccessError):
         await request_handler.call_args[0][0].content.read()
@@ -582,9 +582,10 @@ async def test_keep_alive(make_srv, transport, ceil) -> None:
         b'Host: example.com\r\n'
         b'Content-Length: 0\r\n\r\n')
 
-    await asyncio.sleep(0)
-    waiter = srv._waiter
-    assert waiter
+    waiter = None
+    while waiter is None:
+        await asyncio.sleep(0)
+        waiter = srv._waiter
     assert srv._keepalive_handle is not None
     assert not transport.close.called
 
@@ -681,7 +682,7 @@ async def test_close(srv, transport) -> None:
         b'Host: example.com\r\n'
         b'Content-Length: 0\r\n\r\n')
 
-    await asyncio.sleep(0)
+    await asyncio.sleep(0.05)
     assert srv._task_handler
     assert srv._waiter
 
@@ -721,7 +722,7 @@ async def handle(request):
     assert len(srv._messages) == 2
     assert srv._waiter is not None
 
-    await asyncio.sleep(0)
+    await asyncio.sleep(0.05)
     assert srv._task_handler is not None
     assert srv._waiter is not None
     assert processed == 2
@@ -856,3 +857,4 @@ async def test_two_data_received_without_waking_up_start_task(srv) -> None:
 
     assert len(srv._messages) == 2
     assert srv._waiter.done()
+    await asyncio.sleep(0.01)