The optimization design of an optical-mechanical system has the characteristics of high efficiency and short iteration period, but the optimization of the complex optical-mechanical system has the problem of difficulty in convergence. An approximate optimization algorithm based on the combination of Latin hypercube and radial basis function (RBF) neural network is proposed in this work, and it is applied to the design of main mirror of spliced telescopes with curvature error adjustment mechanism. Simulation results show that the main mirror optimized by the algorithm has reached the design index, which provides a new idea for solving the problem of long iteration time for complex optical-mechanical system.