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A mobile manipulator service robot comprising a mobile platform with a three-link arm mounted on top of the platform is considered. A torque compensation control approach is proposed for the robust motion control of the robot. Considering the coupling disturbance between the platform and the manipulator, the nominal model of service robot is built, applying computed torque and proportion-differential (PD) feedback control method to decouple the control system. Aiming at the modeling uncertainty and existing uncertainties disturbances, compensation is adopted for the built control law. Lyapunov method is adopted to determine the compensation item, and by these, the robust motion control of the mobile manipulator service robot is realized. Simulation experiment had been done for the mobile platform and the manipulator, experiment results show that, the presented control method can realize the robust control of mobile manipulator service robot, and thus show the effectiveness and correctness of the designed controller.