In order to shape aspheric surfaces for ultra-thin spherical mirrors, a new method for the initial solutions of actuator arrangements solved by asphericity gradient was presented.The theoretical analysis, arrangement method and two formulas for calculating the asphericity gradient were given. As shaping an off-axis large-aperture aspheric mirror for example, the initial solutions of actuator arrangements were obtained by two formulas above, respectively. By using Finish Element Method(FEM), the deformation analysis of shaping aspheric surfaces with form error of 21.09 nm was accomplished, and the final solutions were given. Moreorer, the optimizations of actuator arrangements were discussed. Finally, three kinds of methods for actuator arrangements were compared with each other. The results indicate that the initial solution based on average value of asphericity gradient is most similar to the final solution, which is in accord with the relation between the change rate of asphericity gradient and the surface density of actuator arrangements. The optimization can reduce the number of actuators and can improve the form error further. Under the same form error, the number of actuators by the aspheric gradient method is 1/2 or less than that by the square and circular methods; under the same actuator numbers, the RMS of form error by the aspheric gradient method is about 1/3 or less than that by the square and circular methods. These data reported here show that the aspheric gradient method is suitable to solve an initial solution of actuator arrangements in the field of shaping aspheric surfaces.