A Wireless Internet-access Mesh NETwork (WIMNET) can provide an expandable Internet-access network by adopting multiple Access-Points (APs) that have wireless connections with each other. Previously, we proposed a routing tree algorithm for generating an optimal routing path between the APs and the Internet Gate Way (GW) with a minimal transmission delay, assuming that every link has the same data transmission speed. However, our preliminary experiments found that the link speed using the IEEE802.11n as a new high-speed protocol for wireless communications, decreases drastically as the distance increases due to the lowered receiving signal quality. In this paper, we propose a modified routing tree algorithm to consider the large speed change in order to adopt the IEEE 802.11n in WIMNET effectively. In addition to links between APs, our modified algorithm selects the links between hosts and their associated APs. We verify the effectiveness of the modified algorithm through simulations in three topologies.