Abstract: The optical system for OPU(optical pick-up) is a uncoaxial optical system. The design position of optical element and its accurate assembly are critical for the proper operation of the system. Quarternion is a convenient mathematical method to describe the spatial lightbeam propagation and dimensional coordinate transfer. Three types of light-beam propagation in the uncoaxial optical system of OPU were characterized with quarternion, and the arithmetic method of the light propagation for the system was established. With the model, the flow chart for describing the relationship between optical component design, assembly parameter, foucsing spot and readout spot is obtained. This model can be used for analyzing optical assembly error, instructing assembly technicians, simulating the focusing of objective lens or tracking the displacment of objective lens.