This　paper　originally　proposes　a　nonlinear　cohesive/frictional　contact　coupled　model　for　the　mode-II　shear　delamination　of　adhesive　composite　joint　based　on　a　modified　Xu　and　Needleman＇s　exponential　cohesive　model.　First,　the　friction　is　assumed　to　increase　nonlinearly　at　the　delamination　interface　when　the　tangential　cohesive　softening　appears.　Second,　a　non-associative　plasticity　model　based　on　the　Mohr-Coulomb　frictional　contact　law　is　proposed,　which　includes　a　frictional　slip　criterion　and　a　slip　potential　function.　Third,　a　return　mapping　algorithm　based　on　the　non-associative　plasticity　theory　is　proposed　to　solve　the　updated　normal　and　tangential　tractions　and　stiffnesses.　It　is　shown　the　tangential　cohesive　traction　and　stiffness　depend　on　the　friction　and　dilatancy　of　the　delamination　interface.　Finally,　the　proposed　theoretical　model　is　implemented　using　three-dimensional　finite　element　analysis　by　ABAQUS-UEL　(user　element　subroutine)　and　demonstrated　by　comparing　the　finite　element　results　with　the　analytical　results　for　the　[0　degrees](6),　[+/-　30　degrees](5),　[+/-　45　degrees](5)　end-notched　flexure　adhesive　composite　joints　with　the　mode-II　shear　delamination.　The　effects　of　the　friction　coefficient,　cohesive　strength,　normal　contact　stiffness　and　mesh　size　on　the　load-displacement　curves　and　delamination　mechanisms　of　composites　are　studied.　Numerical　results　show　the　shear　delamination　growth　is　governed　by　the　transition　from　the　decreased　tangential　cohesive　traction　to　the　increased　tangential　friction,　and　the　frictional　effect　becomes　distinct　after　unstable　delamination　for　angle-ply　laminates.