The permanent magnet synchronous motor (PMSM) with dual-rotating rotors is a typical nonlinear multi-variable coupled system. It is sensitive to load disturbances and the change of interior parameters. The traditional proportional-integral (PI) controller is widely used in the speed control of a motor because of its simplicity; however, it cannot meet the requirements needed for high performance. In addition, when the loads of both of the rotors change, it is difficult to ensure that the system runs stably. With an aim to mitigate these problems, a method called master-slave motor control is proposed to guarantee the stability of the motor system in all cases. And then, a speed controller is designed to eliminate the influence of uncertain terms. The proposed control strategy is implemented both in simulations and in experiments. Through the analysis and comparison of the proportional-integral (PI) controller and the sliding-mode controller, the effectiveness of the proposed control strategy is validated.