In　a　microgrid,　grid-connected　inverters,　as　the　interface　between　the　distributed　power　supply　and　grid,　cannot　provide　inertia　support　for　the　system.　The　control　strategy　of　virtual　synchronous　generator　(VSG)　based　on　grid-connected　inverters　can　enhance　the　stability　of　system　frequency.　In　order　to　make　the　frequency　response　that　has　a　smaller　overshoot　and　a　shorter　settling　time,　a　self-adaptive　damping　control　strategy　based　on　the　relationship　between　the　damping　and　the　maximum　frequency　deviation　for　microgrid　VSG　is　presented.　The　small-signal　mathematical　model　of　VSG　is　established,　and　the　range　of　the　damping　coefficient　is　determined.　Finally,　simulation　experiments　are　carried　out　with　MATLAB/Simulink,　and　the　effectiveness　of　the　proposed　control　strategy　is　verified　by　comparing　it　with　various　damping　control　methods.