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Many systems are required to execute a series of missions with a finite break between any two adjacent missions. In order to improve the reliability of the system completing the next mission successfully, it is necessary to perform maintenance actions on the components considering limited maintenance resources. A novel idea to solve the problem of selective maintenance for a series-parallel system is proposed in this paper. This problem consists in finding the best choice of maintenance actions on a multi-component system by maximizing the system reliability under limited resources. With the increased number of components in the system, the possible combinations of selective maintenance increase exponentially, which raises the difficulty of the problem. For better solution of the problem, from the perspective of maintenance benefit, we develop a selective maintenance policy under maintenance priority of components. Finally, numerical example of a series-parallel system is given to illustrate the proposed method and verify the correctness and accuracy of the method.