As a scalable, flexible access network to the Internet, we have studied the design optimization and the implementation of the Wireless Internet-access Mesh NETwork (WIMNET). WIMNET is composed of multiple access points (APs) that are connected with each other by wireless communications. At least one AP performs as the gateway (GW) to the Internet. Any host in the network can access to the Internet through this GW, after associating its neighbor AP and communicating with multihop wireless links between APs. The delay along the routing path degrades the performance of WIMNET. To avoid the bottleneck of communications by minimizing the maximum delay, we formulate the routing tree problem for AP communications, and prove the NP-completeness of its decision version. Then, we propose the greedy heuristic algorithm of sequentially selecting one link that minimizes the delay of the predicted tree containing the link. The effectiveness of our algorithm is verified through extensive simulations in instances with 25 APs using the WIMNET simulator.