With　the　increasing　capacity　of　new　energy　in　the　power　system,　new　energy　cannot　provide　support　for　the　system　frequency　directly.　This　characteristic　of　new　energy　affects　the　frequency　stability　of　the　power　system.　Therefore　the　control　strategy　of　a　virtual　synchronous　generator　(VSG)　is　proposed　to　improve　the　frequency　stability　of　the　system.　An　adaptive　virtual　inertia　control　strategy　based　on　an　improved　bang-bang　control　strategy　for　a　micro-grid　is　presented.　On　one　hand,　it　can　make　full　use　of　the　variability　of　virtual　inertia　to　reduce　dynamic　frequency　deviation.　On　the　other　hand,　the　steady-state　interval　of　frequency　and　the　steady-state　inertia　are　set　to　improve　the　system　frequency　stability.　Then　the　stability　analysis　of　the　value　range　of　the　virtual　inertia　is　performed　by　the　small　signal　model　of　the　VSG　for　the　micro-grid.　Meanwhile,　the　ranges　of　virtual　inertia　and　steady-state　inertia　are　determined.　Finally,　Matlab/Simulink　is　applied　to　accomplish　simulation　experiments　to　compare　various　virtual　inertia　control　strategies.　The　results　indicate　the　effectiveness　of　the　proposed　strategy.　©　2019　IEEE.