Abstract: The geosynchronous region is one of the most valuable space environment for application which makes it of great significance to monitor the space debris by optical observation. On the basis of the special dynamical characteristics of geosynchronous orbits, the motion features of GEO space debris were introduced in this paper. Concerning the prediction error of the space target and size of field of view, the success probabilities of "concentric circles search" and "climb stairs search" were calculated. Based on the calculated results, the strengths and weaknesses of each search strategy were analyzed. According to the analysis, the "concentric circles search" is more efficient in most cases.