Aiming at the power quality problem of voltage drop in the microgrid grid-connected system, a battery energy storage dynamic voltage restorer (DVR) based on neuron adaptive control is studied. It is mainly composed of battery, inverter, LC filter and transformer. In order to improve the control performance of the DVR, the neuron adaptive control algorithm is introduced to improve the outer loop voltage PI regulator, and the adaptive adjustment of the outer loop control parameters is realized, thereby obtaining a new double-closed-loop control strategy. Then, combined with the space voltage vector modulation method, the control strategy is achieved. Finally, a grid-connected system model of battery energy storage DVR based on neuron adaptive control is built in MATLAB/Simulink simulation software. Simulation results show that the battery energy storage DVR based on neuron adaptive control can compensate for the voltage drop of the microgrid. It has strong dynamic response capability and anti-interference ability.