Taking the wind-hydrogen storage hybrid microgrid as the research object, we construct a hybrid microgrid system based on wind turbines and hydrogen storage device. The hydrogen storage device mainly includes electrolyzer for hydrogen production, hydrogen container for storing hydrogen, and fuel cell for outputting power. To improve the power supply reliability of the hybrid microgrid and reduce the daily investment cost simultaneously, the capacity of the electrolyzer, hydrogen container and fuel cell in the hydrogen storage device are optimized in our work. Considering the three indicators of daily investment cost, power supply reliability and wind curtailment rate of the hybrid microgrid, we design the working strategy of the hybrid microgrid and construct a optimized capacity model of the wind-hydrogen storage hybrid microgrid. In this paper, improved cat swarm algorithm is proposed to solve the optimized capacity model of the proposed hydrogen storage device. In a numerical example, the effectiveness of the improved cat swarm algorithm in solving the optimized capacity model of the hybrid microgrid is verified, and the rationality of the optimized capacity model of the hybrid microgrid proposed in this paper is also proved.