When surrounded by the heterogeneous networks environment, mobile terminals are often expected to select an optimal network quickly from the detected alternatives to ensure the required or better quality of service. How to reduce the probability of ping-pong effect of the process as much as possible is one of the most prominent challenges. From the two viewpoints of attribute weight and utility value, a flexible hybrid multiple attribute decision making heterogeneous network selection algorithm consisting of FAHP, standard deviation, and GRA is proposed. In this algorithm, comprehensive evaluation value of each candidate network is calculated by integrating attribute weight and utility value. Only the network whose comprehensive evaluation value is larger than that of current network and is at least the preassigned threshold will be chosen as the target network and start the handover process. Otherwise the terminal will remain on the current network. Simulation results show that among the four traffic classes this algorithm can quickly select the most suitable network and significantly reduce the number of vertical handovers and the number of ping-pong effects, compared with other four existing baseline algorithms.