As a flexible inexpensive Internet-access network, we have studied the Wireless Internet-access Mesh NETwork (WIMNET) that is composed of wirelessly interconnected Access-Points (APs). Previously, we proposed the routing tree algorithm to generate a routing path connecting the APs in WIMNET such that the performance can improved by reducing congestions at links around the Internet Gate Way (GW). For this algorithm, we assume that every link has the same constant speed to transmit data packets regardless of its distance However, when we adopt the new high-speed IEEE802. 11n protocol for wireless communications, our preliminary experiments found that the speed decreases drastically as the distance increases. In this paper, we extend the routing tree algorithm in order to consider the link speed change and generate the routing path to the hosts. We show the effectiveness of this extension through simulations in three instances.