To realize high-precision speed tracking control of the gimbal system with harmonic drive， a feedforward compensation method based on the iterative learning control of the position domain is proposed. First， the periodicity characteristics of the load angular speed fluctuation in the position domain， which is caused by the kinematic error of the harmonic drive， are analyzed. According to the analysis results， an iteration compensation method of the position domain is proposed. This method obtains the feedforward compensation signal by accumulating the speed adjustment error signal. The compensation signal compensates the torque to suppress the speed fluctuation. Then， the convergence and iteration termination conditions are obtained by the analysis of the iterative learning algorithm. Finally， the effectiveness and feasibility of the proposed method were verified with simulations and experiments. The results show that the proposed iterative learning feedforward compensation method suppresses the load angular speed fluctuation of the gimbal system by more than 30%. The proposed method is simple to implement and has good velocity fluctuation suppression. Simultaneously， the output torque of the control moment gyro is effectively improved.