In the modular multilevel converter based multi-terminal DC (MMC-MTDC) system, the virtual synchronous generator (VSG) control cannot take into account the problem of DC voltage fluctuation regulation when maintaining the frequency stability of the AC grid. The U²-P DC voltage droop control was introduced into the VSG controller for the receiving-end converter in the MMC-MTDC system, and the VSG control with additional DC voltage was obtained. This control can not only realize the frequency adjustment in the AC region, but also control the DC voltage. By analyzing the influence of moment of inertia in VSG on the frequency response of AC grid, an adaptive virtual moment of inertia adjustment method based on fuzzy control was designed on the basis of additional DC voltage VSG control. By flexibly adjusting the virtual inertia, the converter shows smoother and faster dynamic response performance in the process of supporting frequency fluctuation. The effectiveness of the proposed strategy is verified on the MATLAB/Simulink simulation platform, which shows that the proposed strategy can adjust the frequency and DC voltage at the same time and can show better frequency dynamic response performance.