Aimed at the problem that the charging and discharging state switching frequency is too high and the life is reduced during the process of wind power fluctuation suppression by energy storage, a fluctuation suppression control strategy based on the hybrid energy storage of dual battery packs is proposed. First, the adaptive moving average filter method is used to decompose the wind power to obtain the grid-connected power. Second, the wavelet packet decomposition of the energy storage target power is carried out to obtain the hybrid energy storage reference power, and the fuzzy control is used to optimize the energy storage target power, so as to prevent the energy storage from overcharge or overdischarge and make the energy storage run at the optimal depth of discharge (DOD). To make the battery run at the optimal DOD while reducing the switching times of working states, a circuit structure of dual battery packs running separately for charging and discharging tasks is adopted, and an adaptive power complementary control strategy is designed to realize power scheduling between battery packs. In addition, a power allocation strategy is also introduced to ensure the state-of-charge balance among each unit in the same battery pack. Finally, the control strategy is simulated and analyzed, and the rainflow counting method is used to evaluate the life of energy storage. Results show that the proposed control strategy can reduce the charging and discharging times of energy storage and prolong its life.