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In order to improve the trajectory tracking performance of space robots, it is necessary to consider the influence of various working conditions such as dead zone and friction. To deal with them, a compensator is designed to eliminate the effects of the joint torque dead zone and a dual observer is used to estimate the friction state. In order to suppress the vibration of the links, a virtual control force is proposed. Based on this, a hybrid trajectory control based on recurrent cerebellum model articulation controller neural network (RCMACNN) is designed. This method can not only achieve trajectory tracking, but also suppress flexibly vibration, and at the same time eliminate the vibration coupling between various working conditions. Using Lyapunov function, it is proved that the filtering error is ultimately uniformly bounded (UUB). Finally, a planar space robot with two flexible links is applied for simulation, and the results prove the effectiveness of the method.