The　geometries　and　electronic　structures　of　the　(111)　surfaces　of　some　transition-metal　carbides　MC　(M　=　Ti,　Zr,　V,　Nb)　have　been　investigated　by　using　the　first-principle　methods.　The　results　indicate　that,　compared　to　the　ideal　surface,　the　first　layer　(metal　layer)　and　second　layer　(carbon　layer)　shift　inwards　and　outwards　respectively,　and　as　a　result,　the　space　between　the　first　and　second　layer　is　contracted.　The　results　of　the　band　structure　calculation　show　that　the　main　components　of　the　surface　state　in　DOS　located　near　or　crossed　by　E-F　are　d(xz)/d(yz)　orbitals　of　the　surface　metal　atoms,　and　the　influence　of　the　surface　relaxation　on　this　state　has　been　studied.　In　addition,　discussions　about　the　surface　core-level　shifts　and　the　surface　work　functions　are　also　presented.