It has been demonstrated that choosing an appropriate relay node can improve the transmission rate for the system. However, such system improvement brought by the relay selection may be degraded with the presence of the malicious relay nodes, which are selected but refuse to cooperate for transmissions deliberately. In this paper, we formulate the relay selection issue as a restless bandit problem with the objective to maximize the average rate, while considering the credibility of each relay node, which may be different at each time instant. Then the optimization problem is solved by using the priority-index heuristic method effectively. Furthermore, a low complexity algorithm is offered in order to facilitate the practical implementations. Simulation results are conducted to demonstrate the effectiveness of the proposed trust-based relay selection scheme.