In the off-grid microgrid cluster, the energy storage device is mainly charged and discharged to maintain the stability of the bus voltage and the system power balance. Generally, the voltage and current double closed-loop control and fuzzy control are adopted for the energy storage converter. The traditional double closed-loop control parameters and the scale factor and quantization factor in fuzzy control cannot be adjusted in real time during system operation, resulting in slower dynamic response and weak anti-interference ability of the system. In response to the above problems, this paper proposes an adaptive genetic fuzzy double closed-loop control, which can adjust the PI control parameters in real time by adjusting the quantization factor and the scale factor to optimize the control effect. The simulation platform is built in MATLAB/Simulink and the simulation results show that the adaptive genetic fuzzy double closed-loop control combines the advantages of fuzzy and PI control. Under different working conditions, the system has not only a fast dynamic response, small overshoot, and strong anti-interference ability but also good robustness.