Abstract: Abstract： Control moment gyro（CMG）is one of the significant actuators of spacecraft attitude control system, which can complete the orbit maneuver in high rate, with advantages of large torque control, rapid response, low power consumption and long service life. In this paper, a dynamics model of harmonic drive used in CMG gimbal system is proposed, in which the backlash model of harmonic drive, nonlinear stiffness factor and the efficiency of the reducer are given full consideration. Transmission error is considered in the gear model. Compared with the model without transmission error, the output velocity is more accurate in describing the output curve at low speed. The model of CMG gimbal system is established, and a PID control law is designed to suppress the output transmission error, which is reduced by over 50%. Finally, the effects of the stiffness and damping of harmonic gear on system performances are analyzed based on the simulation model.