The accelerator grid voltage of the ion thruster has an impact on the intensity of the current of accelerator grid. At present, the accelerator grid voltage is chiefly determined through multiple experiments, and the theoretical calculation can only provide the maximum value of accelerator grid voltage. In this paper, the optimum design of the accelerator grid voltage for a dual-stage accelerator ion thruster developed by Lanzhou institute of physics is carried out. Using particle-in-cell method and Monte-Carlo collision method (PIC-MCC method), the effects of five accelerator grid voltages (-150, -180, -200, -250, -300 V) on ion trajectory, beam divergence angle, number and energy of the impingement charge exchange (CEX) ion, and accelerator grid sputtering rate are studied with the specific impulse of 8000 s. The results show that the best accelerator grid voltage is -250 V. Finally, the verification experiment is carried out. The results show that when the accelerator grid voltage is around -250 V, the current of the accelerator grid is small, which verifies the correctness of the numerical simulation.