This paper investigates the problem of robust passivity-based sliding mode control (SMC) for uncertain singular systems with semi-Markov switching and actuator failures. The attention is focused on designing a common sliding surface to weaken the jumping effect and developing a sliding mode controller to accommodate to actuator faults for passification of the singular semi-Markovian jump system. Based on linear matrix inequality technique, sufficient conditions are derived to ensure the closed-loop system to be stochastically admissible and robustly passive. Then the finite-time reachability of the sliding surface is guaranteed by the proposed SMC law. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained result.