The　electronic　structures　of　TiN　bulk　have　been　studied　by　using　different　theoretical　formalisms,　and　the　DFT　method,　especially　the　BLYP　method　can　produce　reasonable　results.　The　band　structure　of　TiN(001)　surface　is　also　investigated　and　two　cr　type　surface　states　are　presented　in　our　results.　The　state　located　at　2.9　eV　below　E-F　in　angle　resolved　photoemission　in　(ARPES)　is　wed　reproduced　in　this　work,　which　consists　essentially　of　2p(z)　orbital　of　surface　N　atom.　Another　surface　state　is　associated　with　the　bands　originated　from　3d　orbital　of　surface　Ti　atom.　Furthermore,　the　elastic　constants　of　TiN　are　also　calculated　by　using　BLYP　method.