The wireless Internet-access mesh network (WIMNET) has been studied to offer an inexpensive, scalable Internetaccess wireless network by adopting multiple access points (APs) connected by wireless links. WIMNET can improve the dependability to failures of links and/or APs by allocating APs redundantly in the network field. However, redundant APs may increase the operational cost and degrade the throughput due to increasing radio interferences. One solution to this problem is to activate only the necessary APs to provide the connectivity to the hosts while maximizing the throughput. In this paper, we first define this active AP selection problem of selecting the activated APs for communications, and propose its heuristic algorithm. The simulation results in three instances confirm the effectiveness of the proposed algorithm, and indicate the existence of an active AP selection that maximizes the throughput. Then, we present the average hop count and the traffic bias as the indices to seek the active AP selection with the maximal throughput, and the extension of our active AP selection algorithm using them.