Electro-hydrostatic actuator is generally regarded as the preferred solution for more electrical aircraft actuation systems. It is of importance to optimize the weight, efficiency and other key design parameters, during the preliminary design phase. This paper describes a multi-objective optimization preliminary design method of the electro-hydrostatic actuator with the objectives of optimizing the weight and efficiency. Models are developed to predict the weight and efficiency of the electro-hydrostatic actuator from the requirements of the control surface. The models of weight prediction are achieved by using scaling laws with collected data, and the efficiency is calculated by the static energy loss model. The multi-objective optimization approach is used to find the Pareto-front of objectives and relevant design parameters. The proposed approach is able to explore the influence of the level length of linkage, displacement of pump and torque constant of motor on the weight and efficiency of the electro-hydrostatic actuator, find the Pareto-front designs in the defined parameter space and satisfy all relevant constraints. Using an electro-hydrostatic actuator for control surface as a test case, the proposed methodology is demonstrated by comparing three different conditions. It is also envisaged that the proposed prediction models and multi-objective optimization preliminary design method can be applied to other components and systems.