diff --git a/tenacity/_asyncio.py b/tenacity/_asyncio.py
index 6b24b2e1..35d7eb93 100644
--- a/tenacity/_asyncio.py
+++ b/tenacity/_asyncio.py
@@ -15,7 +15,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-
+import asyncio
 import sys
 from asyncio import sleep
 
@@ -71,3 +71,9 @@ async def __anext__(self):
                 await self.sleep(do)
             else:
                 return do
+
+    def wraps(self, fn):
+        fn = super().wraps(fn)
+        # Ensure wrapper is recognized as a coroutine function.
+        fn._is_coroutine = asyncio.coroutines._is_coroutine
+        return fn
diff --git a/tenacity/tests/test_asyncio.py b/tenacity/tests/test_asyncio.py
index 617a0ef5..f34a40af 100644
--- a/tenacity/tests/test_asyncio.py
+++ b/tenacity/tests/test_asyncio.py
@@ -58,6 +58,10 @@ async def test_retry(self):
         await _retryable_coroutine(thing)
         assert thing.counter == thing.count
 
+    @asynctest
+    async def test_iscoroutinefunction(self):
+        assert asyncio.iscoroutinefunction(_retryable_coroutine)
+
     @asynctest
     async def test_retry_using_async_retying(self):
         thing = NoIOErrorAfterCount(5)