The light and small pan-tilt system of a multi-rotor unmanned aerial vehicle is a complicated electromechanical servo system that requires a number of desirable properties such as light weight and rapid response to be realized. We focus on the inherent limitations of the traditional methods in the electromechanical servo-system design to present a multi-objective optimization method for a mechatronic system based on the bandwidth. For the structure system, seven-dimensional parameters were selected using sensitivity analysis in which the mass and first-order natural frequency are considered as the optimization goals. For the control system, the controller parameters in the rate and position loops are selected as design variables in which the rise time, regulating time, and integral absolute error (IAE) are considered as the optimization goals. In the optimization process, an optimization method that combines the approximation model and multi-objective genetic algorithm is proposed to reduce the complexity, improve the efficiency, and improve the overall optimization ability during the optimization process. Simulations are then conducted to verify the proposed method. The results show that, compared with the original model of the control and structure systems, the mass, IAE, regulating time, and rise time are reduced by 8.8%, 54.8%, 81.9%, and 53.4%, respectively. Finally, a modal pan-tilt experiment is carried out by hammering, and the error in the experimental and optimization results is found to be 13.4%. Therefore, the optimization method is effective.