In the independent micro-grid containing multi micro-source, the virtual synchronous generator (VSG) control can improve the frequency response characteristics by adopting the fixed inertia, but which cannot act well both in the dynamic adjustment of VSG active power and frequency. To solve this problem, the fuzzy control of inertia (FCI) was proposed in this paper. Firstly, the mathematical model of VSG was established in the synchronous rotating reference frame, in addition, the influence of inertia on the characteristics of VSG was analyzed. Secondly, a fuzzy controller of inertia is designed, and the fuzzy control rules are obtained through the analysis of different operation conditions, so as to realize real-time dynamic adjustment of inertia. Finally, on condition that VSG was put into the micro-grid and load disturbance in isolated grid, the power and frequency response curves of VSG control and FCI control were compared in the simulation environment of Matlab/Simulink. The simulation results show that the proposed strategy can avoid instantaneous power oscillation when VSG was connected into micro-grid, and achieve effective optimization of frequency response curve.