A Wireless Internet-access Mesh NETwork (WIMNET) can provide an expandable Internet-access network by flexibly adopting multiple Access-Points (APs) that have wireless connections in the field. Previously, we proposed a routing algorithm for generating an optimal routing path between the hosts and one Internet Gateway (GW). However, in practical situations, multiple GWs are usually necessary for scalability. Beside, in the high-speed IEEE802.11ac protocol, the link speed drastically decreases as the distance increases due to the lowered receiving signal quality. Furthermore, commercial APs implementing them have the limitation on the number of hops between a GW and a host. In this paper, we propose a routing algorithm to consider these practical conditions for large-scale WIMNET. We verify the effectiveness through simulating three topologies using the WIMNET simulator.