In order to control line-of-sight(LOS) pointing with two-axis fast-steering mirror(FSM) accurately, kinematic equations was set to describe the relationship between LOS pointing and angular displacement of FSM deriving from Snell′s law of reflection. LOS pointing equations were decoupled with non-linear correction. LOS pointing error was less than 8 ?滋rad for two-axis FSM whose tilt angles were both ±20 mrad with beam incidence angle equaling to 45°. LOS pointing accuracy rose 75 times compared with linear approximation. To hold the LOS stationary, rate equations were established in terms of vector rate synthesis to compensate the angular rate of the mounted vehicle in inertial space. Angular rate equations for FSM were simplified via Taylor expansion and high order truncation. The residual angular rate of LOS with different beam incidence angles was calculated, which indicated that the residual error of ?棕Ly was far greater than ?棕Lz. The ratio between residual LOS angular rate and angular rate of mounted vehicle was minimal and less than 0.164% when beam incidence angle was 45°, which satisfied the accuracy requirements. The equations deduced suppliy theoretic reference of position and velocity command generation for FSM control system.