The hybrid energy system that integrates renewable energy technology, energy storage technology with natural gas cogeneration technology is an important way to build a clean, low-carbon, safe and efficient energy system in the future. However, this kind of hybrid energy system is difficult to optimize due to its complex structure, numerous parameters and variables and high coupling degree of multiple supply energy. On the other hand, due to the strong fluctuations of meteorological parameters and user-side demand, the design and optimization of the energy system require detailed simulation and a large number of input data. However, the existing methods can not balance the accuracy and calculation speed in such long-time-scale optimization. Therefore, this study proposes a two-layer global multi-objective co-optimization framework that combines genetic algorithm and the technique for order of preference by similarity to ideal solution based on hourly load throughout a year. The inner layer optimizes the ratio of waste heat distribution and the power of the generating unit with the objectives of operation cost, waste heat utilization rate and grid interaction. The outer layer optimizes the equipment capacity based on the annual cost, primary energy consumption and carbon dioxide emission. The optimal capacity and operation planning of the equipment are determined by the iteration between the inner and outer layers. Furthermore, by comparing with the typical-day optimization scheme, the research finds that the year-round optimization scheme possesses a better overall performance with 3.64% less annual cost, 3.04% less carbon dioxide emission, 17.56% less primary energy consumption and 40.27% less power grid dependence. The above results show that the method this paper proposed can provide effective reference and solution for the study of similar energy system design and operation optimization.