Abstract: This paper considers a multi-state complex repairable system with priority repair discipline, which includes two classes of components, denoted by L1 and L2. L1 is composed of n different types of components in series, whereas L2 contains only one component. The system fails, if the component in L1 fails. If the component in L2 fails, it does not lead to a complete failure, but reduces the effciency of the system. It is assumed that the working time to the two types of components follows different exponential distribution, while the repair time of the repairman follows a general distribution. We derive the system's main steady-state reliability indices using probability analysis, the Laplace transform method, and Tauber's theorem. The instantaneous reliability indices of the system are then estimated by applying Monte Carlo simulation, and the numerical results of special cases verify the correctness of the conclusion. On this basis, this paper also investigates the influence of system parameters on system reliability measures. Furthermore, the sensitivity of the instantaneous reliability and MTTFF value to each parameter is analyzed, and the system's expected profit function per unit time is developed, which provides theoretical support and reference for system reliability designers and decision makers.