Aiming at the problems of poor disturbance immunity and long dynamic response time of the grid-connected inverter based on VSG(virtual synchronous generator) control, an improved fuzzy adaptive control strategy for VSG was proposed. First, a small-signal model of VSG was established to analyze the effects of virtual inertia and damping coefficient on the dynamic response of the system. Determine the value range of the two parameters and use the sparrow search algorithm to optimize the initial values of inertia and damping in the adaptive strategy. Next, the angular frequency change curve of the system after perturbation was analyzed to refine the design fuzzy rules. Finally, a stand-alone VSG model was built in MATLAB/Simulink to compare the different control strategies. The results show that the fuzzy adaptive strategy proposed in this paper not only improves the response speed of the system, but also has a strong anti-disturbance ability when the command power and load power change suddenly. The effectiveness of this paper's strategy is proved.