An on-orbit inspection satellite is a kind of small multi-purpose servicing spacecraft, which can periodically flying around a target spacecraft. It is very useful in on-orbit remote observation, malfunctions detection and maintenance. Observation trajectory design and control is one of the key applied techniques of on-orbit inspection satellite. The on-orbit observation trajectory is formed by the close range visual relative motion between the target satellite and the inspection or chaser satellite. And, it can be divided into natural inspection motion and fast controlled inspection motion. In this paper, the velocity impulse control model for observation trajectory control was established at first; Then, how the typical observation trajectories, which include stationary observation trajectory, straight line oscillation observation trajectory, flyaround football observation trajectory and fast controlled flyaround observation trajectory, formed and their characteristics were analyzed; Finally, the major factors affecting the on-orbit observation trajectory were discussed and some useful conclusions were given. The results indicate that the natural flyaround football motion and the fast controlled flyaround motion are the two effective on-orbit inspection modes and the initial state error and impulse control error are the two dominant factors affecting the on-orbit observation trajectory.