As an important supporting technology for carbon neutrality strategy, the combination of an integrated energy system and hydrogen storage is expected to become a key research direction. To address the insufficient flexibility of multi-energy coupling in the integrated energy system and the overall strategic demand of low-carbon development, a multi-storage integrated energy system architecture that includes electric storage, heat storage and hydrogen storage is established. Then, according to the system status factors, such as energy cost, response characteristics and energy storage status, a hierarchical energy supply control strategy focusing on the energy supply priority of energy storage units is proposed. NSGA-Ⅱ-MOABC is created as the optimization algorithm to meet the demand of multi-energy coupling energy supply in the integrated energy system. Next, considering the system operational cost and carbon emission cost as the optimization goal, a comprehensive energy optimization scheduling model of multi-storage combined hierarchical energy supply is constructed. Based on the simulation example, the scheduling results of the multi-storage combined system are obtained, through comparative analysis, the addition of hydrogen storage can effectively improve the flexibility of system scheduling. Then, taking several scenarios as simulation examples, the hierarchical energy supply strategy can effectively reduce the system operation cost and carbon emission cost, and it also has a certain role in realizing the local consumption of renewable energy.