The maintenance priority indexes-based (MPIs-based) selective maintenance policy (SMP) for a complex system with degradation components is studied in this work. The SMP is performed in a scheduled break when the system just completed the current mission. During the break, the MPIs, including maintenance importance, structure importance, and reliability importance, are comprehensively considered to support the system for executing the next mission. The objective of the MPIs-based SMP is to find the optimal maintenance decision for the system subject to maintenance cost and time constraints. Besides, the maintenance quality related to component degradation, as well as the economic dependence, are also considered as the maintenance information to be integrated when performing a maintenance decision. The complicated optimization problem is solved by using a simulated annealing algorithm (SAA). The simulation example of an aero-engine control system is presented to depict the maintenance decision process and illustrate the advantage of MPIs-based SMP.