To solve the coupling problem between the compensators during the computer-aided alignment of a reduced projection system with primary and secondary mirrors and to select the compensators properly, a computer-aided alignment algorithm based on singular value decomposition of an optical system sensitive matrix was described. An alignment model for the reduced projection system was established, and both of the algorithm and the model were accomplished in the experiment. An aspherical surface figure detected with a null lens was introduced into the CODE V optical model，the analysis of the sensitivity matrix was used to supervise the optimization of the optical system, and the optimized structural parameters were considered as the benchmark of the assembly and positioning of optical and mechanical system. The experiments show that the created system alignment model is closer to the actual alignment process，and efficiently supervises system alignment，solves the coupling problem between the compensators, and accelerates the convergence process. Finally, computer-aided alignment experiment was completed based on a self-developed interferometer with high precision.It shows that the system wavefront error is minished from 46.39 nmRMS to 20.73 nmRMS, which verifies the veracity of the algorithm and the alignment model.