For improving the accuracy under P2P networks, it must be assured that all non-faulty peers can reach agreement. As such, all the non-faulty peers need to work collaboratively despite disturbances caused by faulty peers. This agreement issue is usually called as the Byzantine Agreement (BA) problem. In previous works, (n-1)/3 + 1 bouts for exchanging message are necessary to allow all non-faulty peers reaching an agreement. Furthermore, the message complexity of these algorithms are O(n n ). Hence, the relevant algorithms are not suitable for mobile P2P networks in which there may have a great quantity of mobile peers. In this study, a more efficient algorithm has been proposed to decrease the required bouts for exchanging message. Our proposed algorithm only need to run three bouts for exchanging message to allow all nonfaulty peers to reach an agreement despite some peers roaming among the different network. It also can decrease the message complexity to O(n 2 ). It is more suitable and efficient than previous efforts aimed at the mobile P2P network.