Recently, virtual synchronous generators (VSGS) are a hot topic in the area of microgrid control. However, the traditional fixed-parameter-based VSG control methods have an obvious disadvantage. Namely, if the damping value is set to be small, the amplitude of frequency deviations under external power disturbances is large, meaning that the frequency suppression capacity is insufficient, but if the damping value is large, the dynamics of the system will be greatly sacrificed. To solve the problem, taking the dynamic characteristics and the maximum allowable frequency deviation (MAFD) into account, in this paper an improved fuzzy adaptive damping-based VSG control strategy is proposed to simultaneously attenuate the microgrid frequency fluctuations and guarantee the system dynamics. Firstly, in order to address the necessity of using an adaptive damping-based VSG, the structure of a fixed-parameter VSG method that incorporates the f-p/Q-V droop controllers is introduced, based on which a small signal model is established to discuss the impacts of the virtual damping on the frequency response characteristics concerning the different penetration levels of power disturbances. Then, considering the dynamics and MAFD, a fuzzy adaptive controller is constructed relying on the well-designed membership functions, control rules and output scaling factors. The main feature of the improved fuzzy controller is that two alternative output scaling factors are employed to allow the system to be overdamped when the frequency deviation is large and undamped when the frequency deviation is small, balancing the frequency response dynamics and stability characteristics. To verify the effectiveness of the proposed fuzzy adaptive damping-based VSG technique, a computer simulation is conducted on a microgrid system in MATLAB/Simulink, and the obtained results are compared with the conventional droop control and fixed-parameter based VSGs. By using the proposed fuzzy adaptive damping-based VSG control method, the peak frequency deviations under the large power disturbances would become at least 8% lower compared to the traditional droop control and fixed-parameter VSG control, and meanwhile, the frequency response speed is fast when the disturbance stands at a low position. Consequently, it is valuable to promote the proposed techniques in engineering.