This raper presents a new optimization method combining the genetic algorithm with the response surface method for the optimum design of a Brushless Direct Current motor. The method utilizes a regression function approximating an objective function and the window moving and zoom-in method so as to complement disadvantages of both the genetic algorithm and response surface method. The results verify that the proposed method is powerful and effective in reducing cogging torque by optimizing only a few decisive design factors compared with the conventional stochastic methods.