Electro-hydrostatic actuators (EHAs) combine the advantages of electric and hydraulic actuators, and it is resulting in a preferable solution for the heavy load actuation in applications such as aircrafts, ships, construction machines, and machine tools. The required power level of the EHA is increasing because the EHA is being introduced to heavier vehicles such as submarines and heavy launch vehicles. Thus, a 30 kW EHA is under development for launch vehicles, which simultaneously require high dynamic performance, light weight, high efficiency, etc. However, the existing optimization design methods of EHA do not take in account all the requirements, especially the dynamic performance. Therefore, a dedicate multi-objective optimization design method is proposed for the preliminary design for the 30 kW EHA. In this study, firstly, the design requirements were analyzed for the launch vehicle application, and the objectives and the constraints of the optimization design were defined for the 30 kW EHA. Secondly, dedicate models were developed for evaluating each objective or constraint. Among these models, the EHA weight is estimated through the scaling law method and analytical calculation, the bandwidth is estimated based on the cascaded control method, the energy consumption is evaluated by the inverse dynamic simulation utilizing dedicate Matlab codes. Thirdly, the multi-objective EHA optimization design was implemented based on the genetic algorithm. Hereby, the key parameters were decided for the proposed EHA design. At last, the optimization design results were evaluated through simulation analysis, which demonstrated that the 30 kW EHA achieved more than 10 Hz bandwidth with under 70 kg weight while the efficiency was also optimized. In addition, the proposed method is shown to be competent for the preliminary design of high power EHAs which are subject to multiple critical requirements.