To improve the convergence speed of adaptive optics (AO) system controlled by genetic algorithm (GA), a new 19-element AO system model based on GA is set up. The system chooses the first 10-order Zernike mode coefficients on the deformable mirror (DM) as the optimization function, rather than the 19 voltages on the DM. The transform matrix between the 19 voltages and the first 10-order Zernike mode coefficients was deduced and comparative mathematic simulations were done. The simulation shows that the correction ability of the proposed AO system is much better than that optimizing the 19 voltages. Moreover, compared with the GA optimizing DM voltages, the convergence speed of GA optimizing Zernike mode coefficients is improved by more than five times.