diff --git a/Lib/asyncio/sslproto.py b/Lib/asyncio/sslproto.py
index 31803ac3b0dc8f..61d478ebda6c78 100644
--- a/Lib/asyncio/sslproto.py
+++ b/Lib/asyncio/sslproto.py
@@ -685,12 +685,14 @@ def _fatal_error(self, exc, message='Fatal error on transport'):
             self._transport._force_close(exc)
 
     def _finalize(self):
+        self._sslpipe = None
+
         if self._transport is not None:
             self._transport.close()
 
     def _abort(self):
-        if self._transport is not None:
-            try:
+        try:
+            if self._transport is not None:
                 self._transport.abort()
-            finally:
-                self._finalize()
+        finally:
+            self._finalize()
diff --git a/Misc/NEWS b/Misc/NEWS
index 05331939f6efe4..5edf13b98cdb94 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -56,6 +56,9 @@ Extension Modules
 Library
 -------
 
+- bpo-29870: Fix ssl sockets leaks when connection is aborted in asyncio/ssl
+  implementation. Patch by Michaël Sghaïer.
+
 - bpo-29743: Closing transport during handshake process leaks open socket.
   Patch by Nikolay Kim