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To invade a cyber-physical system (CPS) successfully, hackers are prone to simultaneously launching multiple cyber attacks on different sensors in a CPS. However, little attention has been paid to the problem of detecting multiple cyber attacks up to now. Therefore, in this paper, we deal with the problem on how to efficiently detect multiple cyber attacks aiming at different sensors in CPSs. To achieve the goal of simultaneously detecting both the number of attacks and the attacked sensors, we formulate this problem via a random finite set (RFS) theory, and then apply an iterative RFS-based Bayesian filter and its approximation to solve the problem. Four numerical experiments with different attacks are provided, and the results have demonstrated the effectiveness of the RFS-based approach for the problem of multiple attacks detection in CPSs.