Carbon　nanotube　(CNT)　can　be　used　as　a　good　reinforcement　embedded　into　polymer　matrix.　However,　properties　of　composites　reinforced　by　CNT　can＇t　be　improved　efficiently,　because　of　the　damage　of　interface　between　CNT　and　polymer　in　CNT　composites.　In　this　paper,　the　cohesive　zone　model　(CZM)　was　employed　to　express　the　damage　and　fracture　of　interface　between　CNT　and　the　epoxy　matrix.　The　key　parameters　of　the　bilinear　CZM　were　deduced　based　on　the　existing　theory　work.　The　whole　deformation　and　fracture　process　of　the　interface　has　been　revealed　through　the　FE　simulation　results.　The　performance　of　the　interface　decides　the　mechanical　property　of　the　CNT　composites　and　the　stress-strain　curve　of　composites　has　been　plotted.　It　is　with　great　importance　to　study　the　mechanical　property　of　the　interface　to　improve　the　performance　of　CNT　composites.