In space laser communication, the composite axis system (CAS), consisting of the coarse tracking system (CTS) and the fine tracking system (FTS), accomplishs the wide ranging and high accurate tracking tasks. The digital simulation of CAS based on Z transform is given to study the bandwidth design of the CAS. According to the trajectory of the satellite and the mechanical error of the CTS, the bandwidth design of CTS is obtained. Moreover, the cooperation of CTS and FTS is given, and the bandwidth design of FTS is gained. At last, the bandwidth design of CAS with disturbance of medium and high frequency is presented. The results above present the theoretical basis for the design of CAS control system.