In order to improve the pointing precision of the laser-pointing system to moving objects, the motion characteristics of moving targets and the calculation precision of different ahead-point algorithms are studied. According to the movement rules of spacecrafts and celestial bodies, the orbit-dynamics model of the spacecraft is built in the horizontal coordinate system based on the two-line-element (TLE) ephemeris, and the change rules of slant-range, angle, angular speed and angular acceleration are studied. According to the theoretical orbital data, the change rules of the 1st-order and the 2nd-order ahead-points of the laser-pointing system are analyzed. As for the actual non-time-continuous system, the error analysis of ahead-point with backward-difference method and central-difference method is carried out, respectively. The result shows that the angular speed, the angular acceleration and the jerk and other high-order terms of objects have all direct effects on the ahead-point, and the central-difference method is more advantageous.