diff --git a/Lib/asyncio/sslproto.py b/Lib/asyncio/sslproto.py
index 61d31a3b295..a7f1e61596d 100644
--- a/Lib/asyncio/sslproto.py
+++ b/Lib/asyncio/sslproto.py
@@ -546,8 +546,11 @@ class SSLProtocol(protocols.Protocol):
     def _start_shutdown(self):
         if self._in_shutdown:
             return
-        self._in_shutdown = True
-        self._write_appdata(b'')
+        if self._in_handshake:
+            self._abort()
+        else:
+            self._in_shutdown = True
+            self._write_appdata(b'')
 
     def _write_appdata(self, data):
         self._write_backlog.append((data, 0))
diff --git a/Lib/test/test_asyncio/test_sslproto.py b/Lib/test/test_asyncio/test_sslproto.py
index f1771c5561a..bcd236ea263 100644
--- a/Lib/test/test_asyncio/test_sslproto.py
+++ b/Lib/test/test_asyncio/test_sslproto.py
@@ -42,6 +42,7 @@ class SslProtoHandshakeTests(test_utils.TestCase):
             sslpipe.do_handshake.side_effect = mock_handshake
         with mock.patch('asyncio.sslproto._SSLPipe', return_value=sslpipe):
             ssl_proto.connection_made(transport)
+        return transport
 
     def test_cancel_handshake(self):
         # Python issue #23197: cancelling a handshake must not raise an
@@ -95,6 +96,20 @@ class SslProtoHandshakeTests(test_utils.TestCase):
         test_utils.run_briefly(self.loop)
         self.assertIsInstance(waiter.exception(), ConnectionAbortedError)
 
+    def test_close_during_handshake(self):
+        # bpo-29743 Closing transport during handshake process leaks socket
+        waiter = asyncio.Future(loop=self.loop)
+        ssl_proto = self.ssl_protocol(waiter)
+
+        def do_handshake(callback):
+            return []
+
+        transport = self.connection_made(ssl_proto)
+        test_utils.run_briefly(self.loop)
+
+        ssl_proto._app_transport.close()
+        self.assertTrue(transport.abort.called)
+
     def test_get_extra_info_on_closed_connection(self):
         waiter = asyncio.Future(loop=self.loop)
         ssl_proto = self.ssl_protocol(waiter)
diff --git a/Misc/NEWS b/Misc/NEWS
index c01363955dc..1bc38b7bd2c 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -350,6 +350,9 @@ Extension Modules
 Library
 -------
 
+- bpo-29743: Closing transport during handshake process leaks open socket.
+  Patch by Nikolay Kim
+
 - bpo-27585: Fix waiter cancellation in asyncio.Lock.
   Patch by Mathieu Sornay.