To meet the requirement of step accuracy for the scanning mirror of a Differential Optical Absorption Spectroscopy (DOAS) mounted on a geosynchronous orbit satellite, the design of a scanning mirror control system with high accuracy is proposed that specifically considers structural and circuit design aspects. In this scheme, the scanning mirror system was controlled by the master controller that received instructions and sended back information about the current position of the scanning mirror. The scanning mirror controled circuit outputs power through the LMD18200 driver chip. Then, the driver consisting of a stepping motor and harmonic reducer drived the scanning mirror to rotate, and the encoder readed the position information of the scanning mirror. In this study, a method of setting the duty cycle of the PWM was proposed, and the control and elimination methods of the harmonic gear transmission hysteresis were studied. Experimental results show that the mean deviation of the step angle of the system is less than 1″, the maximum deviation is less than 5″, and the standard deviation is less than 2″. This control system design satisfies the requirements of step accuracy for the scanning mirror and provides a reference for related applications on subsequent satellite payload.