To reduce the impact of intermittency and volatility of offshore wind power on the power grid, energy storage devices are often introduced to smooth out its output power fluctuations. In response to the low-carbon development process and considering the uncertainty of wind power, the capacity allocation method for energy storage based on a typical wind power output scenario has limitations. Taking into account the electricity sales revenue, carbon trading revenue, and various costs of the energy storage system of offshore wind farms, a capacity allocation method for hybrid energy storage system of offshore wind farm considering wind power uncertainty is proposed. The random opportunity constrained programming method is adopted to deal with the uncertainty of offshore wind power output, and wavelet packet decomposition method is used to allocate power between lithium batteries and supercapacitors, the allocation scheme is combined with economic evaluation to establish an optimized operation model for wind and energy storage system, with the goal of maximizing the daily net profit of the system, optimizing its capacity configuration. Taking the measured data of a domestic offshore wind farm as an example for simulation, the effectiveness and economy of the proposed scheme are verified. At the same time, the system adopting hybrid energy storage is more superior than single energy storage.