The stochastic parallel gradient descent (SPGD) algorithm can optimize the system performance directly, while being independent of wave-front sensor. Based on SPGD algorithm, an adaptive optics system model with a 32-element deformable mirror was simulated. Convergence of SPGD algorithm was verified through analyzing correction capabilities for static wave-front aberrations. The relationship of algorithm gain coefficient, stochastic perturbation amplitude and convergence rate were discussed. Convergence rate can be improved by adaptive adjustment of algorithm gain coefficient.