Precision beam pointing is the key indicator for APT (acquisition, pointing and tracking) system in space laser communication. The laser travels inside the optical system and the pointing vector will be affected by an assembly error of the axis and reflectors. In this paper, the model of the optical path pointing error and coaxiality error induced by the assembly error are established; the error distribution is given and a quantitative analysis is performed. The results show that the magnitude of pointing error is affected by the axis assembling error greatly but its distribution is susceptible to the reflector assembly error. Finally, the correction of coaxiality is performed and tested. The experimental results show that the coaxiality error can be greatly improved and the mean value of the coaxiality error of a beacon path and a signal path are 14 and 9.6 mu rad, respectively, which meets the requirements. This work can provide guidance for design and assembly of the APT and contribute to the improvement of its pointing performance.