In order to offer an inexpensive, scalable Internet-access wireless network, we have studied the architecture, protocols, and design optimizations of the wireless Internet-access mesh network (WIMNET) that adopts 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. Because redundant APs may increase the operational cost and degrade the throughput due to increasing radio interferences, only the necessary APs for the connectivity between the hosts and the Internet gateway should be activated in communications. Previously, we have defined the active AP selection problem of selecting the minimum number of active APs, and proposed its heuristic algorithm. However, the throughput should be maximized in WIMNET as a band-limited wireless network, even if the number of active APs is slightly increased. In this paper, we propose the extension of the active AP selection algorithm for the throughput maximization using the average hop count. We confirm the effectiveness of our algorithm extension through simulations in three instances, where the throughput is improved by about 10% with 7-14 additional active APs on average.