Summary: A two-stage sliding mode control method with variable boundary layer thickness is proposed for joint fast tracking control of space robot system. Firstly, the object of study is modeled and the dynamic equation of the system is deduced by Lagrange method. Considering the rigid-flexible mixing characteristics, combined with the singular perturbation theory, the system is decomposed into two subsystems: fast subsystem and slow subsystem. A velocity difference feedback control method is designed for fast subsystem, a two-stage sliding mode control method is designed for slow subsystem, and a saturation function with variable boundary layer thickness is introduced to solve the oscillation problem of the system. Finally, it is verified by numerical simulation.