diff --git a/Lib/asyncio/base_events.py b/Lib/asyncio/base_events.py
index 60a189bdfb7ec9..c6054623753d67 100644
--- a/Lib/asyncio/base_events.py
+++ b/Lib/asyncio/base_events.py
@@ -929,29 +929,26 @@ async def create_connection(
                     flags=flags, loop=self)
                 if not laddr_infos:
                     raise OSError('getaddrinfo() returned empty list')
+            else:
+                laddr_infos = [(None, None, None, None, None)]
 
             exceptions = []
-            for family, type, proto, cname, address in infos:
+            for addrinfo, laddrinfo in itertools.product(infos, laddr_infos):
+                family, type, proto, cname, address = addrinfo
+                laddr = laddrinfo[4]
                 try:
                     sock = socket.socket(family=family, type=type, proto=proto)
                     sock.setblocking(False)
-                    if local_addr is not None:
-                        for _, _, _, _, laddr in laddr_infos:
-                            try:
-                                sock.bind(laddr)
-                                break
-                            except OSError as exc:
-                                msg = (
-                                    f'error while attempting to bind on '
-                                    f'address {laddr!r}: '
-                                    f'{exc.strerror.lower()}'
-                                )
-                                exc = OSError(exc.errno, msg)
-                                exceptions.append(exc)
-                        else:
-                            sock.close()
-                            sock = None
-                            continue
+                    if laddr is not None:
+                        try:
+                            sock.bind(laddr)
+                        except OSError as exc:
+                            msg = (
+                                f'error while attempting to bind on '
+                                f'address {laddr!r}: '
+                                f'{exc.strerror.lower()}'
+                            )
+                            raise OSError(exc.errno, msg)
                     if self._debug:
                         logger.debug("connect %r to %r", sock, address)
                     await self.sock_connect(sock, address)
diff --git a/Lib/test/test_asyncio/test_base_events.py b/Lib/test/test_asyncio/test_base_events.py
index 53854758a27d4c..b3f359da402d05 100644
--- a/Lib/test/test_asyncio/test_base_events.py
+++ b/Lib/test/test_asyncio/test_base_events.py
@@ -1367,6 +1367,44 @@ def getaddrinfo_task(*args, **kwds):
         self.assertRaises(
             OSError, self.loop.run_until_complete, coro)
 
+    @patch_socket
+    def test_create_connection_socket_bind_different_family(self, m_socket):
+        # https://bugs.python.org/issue35302
+        # Test the case where local_addr resolves to multiple addrinfos, and
+        # if the socket is bound to the first address, connect() will fail.
+        sock = m_socket.socket.return_value
+
+        self.loop._add_reader = mock.Mock()
+        self.loop._add_reader._is_coroutine = False
+        self.loop._add_writer = mock.Mock()
+        self.loop._add_writer._is_coroutine = False
+
+        def mock_connect_check_bind(address):
+            if sock.bind.call_count:
+                bind_addr = sock.bind.call_args[0][0]
+                if bind_addr[0][:4] != address[0][:4]:
+                    raise OSError
+
+        sock.connect.side_effect = mock_connect_check_bind
+
+        async def getaddrinfo(host, port, *args, **kwargs):
+            if host == 'bindaddr':
+                return [(2, 1, 6, '', ('192.0.2.1', port)),
+                        (10, 1, 6, '', ('2001:db8::1', port))]
+            else:
+                return [(10, 1, 6, '', ('2001:db8::1:1', port))]
+
+        self.loop.getaddrinfo = getaddrinfo
+
+        coro = self.loop.create_connection(
+            MyProto, 'connectaddr', 80, local_addr=('bindaddr', 0))
+        t, p = self.loop.run_until_complete(coro)
+        try:
+            sock.connect.assert_called_with(('2001:db8::1:1', 80))
+        finally:
+            t.close()
+            test_utils.run_briefly(self.loop)
+
     @patch_socket
     def test_create_connection_bluetooth(self, m_socket):
         # See http://bugs.python.org/issue27136, fallback to getaddrinfo when
diff --git a/Misc/NEWS.d/next/Library/2019-03-31-14-50-10.bpo-35302.IDJZzC.rst b/Misc/NEWS.d/next/Library/2019-03-31-14-50-10.bpo-35302.IDJZzC.rst
new file mode 100644
index 00000000000000..bb6ddbcffc7102
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-03-31-14-50-10.bpo-35302.IDJZzC.rst
@@ -0,0 +1,2 @@
+Try each (remote addrinfo, local addrinfo) pair in
+BaseEventLoop.create_connection().