In this paper, based on deformable mirrors and the stochastic parallel-gradient-descent (SPGD) algorithm, an adaptive optics system (AOS) without wavefront detection is theoretically simulated. In order to improve the convergence speed of the AOS without reducing its accuracy, this paper optimizes the relationship between the amplitude of random perturbation and the gain coefficient in the SPGD algorithm. The experiment conducted in this study shows that the AOS has a parameter preference area, which is related to the initial distortion magnitude. Furthermore, the results of the theoretical verification and the comparison with that by the simulated annealing algorithm reveal that the convergence accuracy of the SPGD algorithm is 6.32% higher than that of the SA algorithm and the SPGD algorithm has a larger convergence speed.