To improve the control accuracy of optoelectronic imaging equipment, the factors that affect the accuracy of the optoelectronic axis pointing are analyzed. Following Snell’s law, the kinematic coupling equation of the line-of-sight (LOS) angle based on the fast steering mirror (FSM) is established. The calibration method of the FSM system is designed according to the obtained motion characteristics, and a nonlinear correction method is designed to decouple the LOS equation. For a two-axis fast mirror with a stroke of ±20  mrad, the LOS pointing error is <1  μrad when the incident angle is 45 deg, which equates to an improvement of at least 78.9 times compared with linear correction methods. The nonlinear correction method is verified by practical experiments. The method provides a theoretical basis for generating position instructions and thus enables a precise FSM-based pointing system.