In this paper, we present a design of two-way communication system with relay selection in two-way cooperative system over cascaded Nakagami- fading channels. In the proposed scheme, in which all terminals are in motion as mobiles or vehicles, two users first broadcast their information to relays. Then, a single relay with a minimum sum symbol error rate (SER) will be selected to broadcast the received signals back to the sources. In other words, in the selection process, we investigate a simple suboptimal min-max criterion for relay selection, where a single relay that minimizes the maximum SER of two source nodes will be selected. Specifically, we have derived expressions of cumulative distribution function and moment generating function of end-to-end signal-to-noise ratio. By using these expressions, we have analyzed the performance of considered system in terms of outage probability and SER expression. Numerical and simulation results show the validity of the proposed mathematical analysis and point out the confirmation of the analytical results.