Aiming at the surge and rotating stall of the aero-engine compressor, this paper is concerned with the design scheme of backstepping sliding mode control. First, in order to solve the adverse effects of surge or rotating stall, a compressor model with steady air injection as the actuator is established. Next, based on the basic principles of backstepping control and sliding mode control, the control system is designed according to Lyapunov stability, and appropriate control parameters are selected to make the designed control system asymptotically stable. In the end, an active stability controller of backstepping sliding mode algorithm is designed. Finally, it is verified by simulation. The simulation results show that the designed controller can effectively suppress the unstable disturbance of the compressor in the initial state, and has faster response time and stronger robustness to external disturbances than other algorithms.