The wireless Internet-access mesh network (WIMNET) has been studied to realize the inexpensive, scalable Internet-access network by adopting multiple access points (APs) connected by wireless links. WIMNET can improve the dependability to failures of APs and/or links by allocating APs redundantly, whereas redundant APs may cause the increase of the operational cost and the degradation of the throughput due to increasing radio interferences. Therefore, we have formulated the active AP selection problem of selecting the minimum number of active APs among redundant APs in WIMNET and proposed its heuristic algorithm. The simulation results indicated the existence of an active AP selection maximizing the throughput whose number of active APs is larger than the minimum. In this paper, we improve this algorithm for the throughput maximization. We verify the effectiveness of our algorithm improvement through simulations in three instances.