An optimal allocation approach of servers for improving the performance of P2P networks is proposed in this paper. The approach is to allocate a limited number of servers over the P2P networks to satisfy as many peers as possible, by using a constrained optimization algorithm. In considering that the polar space is more suitable to express length-related constraints, such as those in this approach, a heuristic algorithm based on the polar coordinator mapping is proposed to deal with the optimization problem of the server allocation. Compared with the existing heuristic algorithms that are based on penalty functions, this algorithm can effectively reduce the search space, and the performance is better especially in a high dimensional search space. The experiment results show that our server allocation approach can satisfy more peers' requirement and effectively improve the performance of P2P networks.