The　electronic　structures　of　the　NbC　bulk,　(001)　and　(111)　surfaces　have　been　investigated　by　the　DFT/BLYP　method.　The　results　show　that,　for　the　NbC(001)　surface,　the　surface　state　is　mainly　located　about　4.5eV　below　the　Fermi　level(E-F),　which　is　derived　from　the　surface　of　Nb　4d　and　C　2p　characters.　When　the　oxygens　are　adsorbed　on　NbC(001)　surface,　the　oxygen　atoms　prefer　to　attach　on　the　surface　of　Nb　atoms.　For　the　NbC(111)　surface,　the　surface　states　are　centered　in　the　range　of　0.0　similar　to2.0eV　below　E-F.　The　state　located　just　below　E-F　consists　mainly　of　4d(xa)/d(yz)　orbits　of　Nb　surface　and　it　can　be　ascribed　to　an　＂active＂　surface　state.　However,　since　the　Nb　atom　has　more　d　electrons,　the　component　of　this　＂active＂　surface　state　differs　from　that　of　TiC(111)　surface.　Our　results　calculated　are　in　agreement　with　the　experimental　photoemission　spectra.