The optimal design of the hybrid energy system can significantly improve the economical and technical performance of power supply. However, the problem is formidable because of the uncertain renewable energy supplies, the uncertain load demand, the nonlinear characteristics of some components, and the conflicting techno-economical objectives. In this work. the optimal design of the hybrid energy system has been formulated as a multi-objective optimization problem. We optimize the techno-economical performance of the hybrid energy system and analyse the trade-offs between the multi-objectives using multi-objective genetic algorithms. The proposed method is tested on the widely researched hybrid PV-wind power system design problem. The optimization seeks the compromise system configurations with reference to three incommensurable techno-economical criteria, and uses an hourly time-step simulation procedure to determine the design criteria with the weather resources and the load demand for one reference year. The well-known efficient multi-objective genetic algorithm. called NGAS-II (the fast elitist non-dominated sorting genetic algorithm), is applied on this problem. A hybrid PV-wind power system has been designed with this method and several Methods in the literature. The numerical results demonstrate that the proposed method is superior to the other methods. It can handle the optimal design of the hybrid energy system effectively and facilitate the designer with a range of the design solutions and the trade-off information. For this particular application, the hybrid PV-wind power system using more solar panels achieves better technical performance while the one using more wind power is more economical.