The battery and supercapacitor hybrid energy storage system can not only fully utilize the physical characteristics of power-type energy storage devices, but also optimize the charging and discharging process of batteries, and it is one of the development trends of energy storage technology in the future. A dual decoupling control strategy with master-slave structure is proposed to meet the requirements in isolated operation of microgrid. The coupling relationship between bus voltage and disturbance input is eliminated by power feedforward, and the influence of coupling disturbance input on the terminal voltage of supercapacitor is restrained, thus allowing the terminal voltage to be effectively maintained in a norm. The problem of supercapacitor overcharge and overdischarge under the traditional control strategy is solved, and the control process is simplified. The stable operation of the microgrid is ensured, the charging and discharging current of the batteries changes smoothly, the change rate of the output current of the batteries decreases, and the service life of the batteries is prolonged. The reliability of the micro-grid island operation energy storage system is improved. Finally, simulation analysis is carried out and the correctness of the proposed control strategy is verified.