Multi-terminal　high　voltage　direct　current　transmission　based　on　voltage　source　converter　(VSC-HVDC)　grids　can　connect　non-synchronous　alternating　current　(AC)　grids　to　a　hybrid　alternating　current　and　direct　current　(AC/DC)　power　system,　which　is　one　of　the　key　technologies　in　the　construction　of　smart　grids.　However,　it　is　still　a　problem　to　control　the　converter　to　achieve　the　function　of　each　AC　system　sharing　the　reserve　capacity　of　the　entire　network.　This　paper　proposes　an　improved　control　strategy　based　on　the　slope　control　of　the　DC　voltage　and　AC　frequency　(V-f　slope　control),　in　which　the　virtual　inertia　is　introduced.　This　method　can　ensure　that　each　AC　sub-system　shares　the　primary　frequency　control　function.　Additionally,　with　the　new　control　method,　it　is　easy　to　apply　the　secondary　frequency　control　method　of　traditional　AC　systems　to　AC/DC　hybrid　systems　to　achieve　the　steady　control　of　the　DC　voltage　and　AC　frequency　of　the　whole　system.　Most　importantly,　the　new　control　method　is　better　than　the　traditional　control　method　in　terms　of　dynamic　performance.　In　this　paper,　a　new　control　method　is　proposed,　and　the　simulation　model　has　been　established　in　Matlab/Simulink　to　verify　the　effectiveness　of　the　proposed　control　method.