Aiming　at　the　problem　that　the　bus　voltage　in　a　low-inertia　DC　microgrid　is　prone　to　be　affected　by　internal　power　fluctuations,　an　adaptive　virtual　inertia　control　strategy　for　a　grid-connected　converter　of　a　DC　microgrid　based　on　an　improved　model　prediction　is　proposed.　Firstly,　the　adaptive　analog　virtual　synchronous　generator　(AVSG)　is　introduced　into　the　voltage　outer　loop　by　combining　the　inertial　parameters　with　the　voltage　change　rate,　and　the　flexible　adjustment　of　the　inertial　parameters　is　realized.　Secondly,　the　improved　model　predictive　control　is　introduced　into　the　current　inner　loop　to　realize　the　fast-tracking　of　the　given　current　value　and　improve　the　dynamic　characteristics　of　the　control　system.　Finally,　a　system　model　is　established　based　on　Matlab/Simulink　for　simulation.　The　results　show　that　compared　with　the　traditional　virtual　inertia　control　strategy,　the　proposed　control　strategy　has　smaller　bus　voltage　fluctuation　amplitude　and　better　dynamic　performance;　when　a　10　kW　load　mutation　occurs,　the　magnitude　of　bus　voltage　drop　is　reduced　by　60%,　and　the　voltage　recovery　time　is　shortened　by　30%.　The　proposed　control　strategy　can　effectively　improve　the　stability　of　DC　bus　voltage　and　the　operation　ability　of　the　system　under　asymmetric　conditions.