An　r-uniform　hypergraph　is　linear　if　every　two　edges　intersect　in　at　most　one　vertex.　Given　a　family　of　r-uniform　hypergraphs　F,　the　linear　Turan　number　ex(r)(lin)(n,　F)　is　the　maximum　number　of　edges　of　a　linear　r-uniform　hypergraph　on　n　vertices　that　does　not　contain　any　member　of　F　as　a　subhypergraph.　Given　a　graph　F　and　a　positive　integer　r　＞=　2,　the　r-expansion　of　F　is　the　r-graph　F+　obtained　from　F　by　enlarging　each　edge　of　F　with　r　-2　new　vertices　disjoint　from　V(F)　such　that　distinct　edges　of　F　are　enlarged　by　distinct　vertices.　For　t　＞=　s　＞=　2,　we　prove　the　following　extension　of　Kovari-Sos-Turan＇s　theorem　ex(r)(lin　)(n,　K-s,t(+))　＜=　(t-1)(1/s)/r(r-1)　.n(2-1/s)　+　O(n(2-2/s)).　Specially,　for　s　=　2,　r　=　3,　we　prove　that　ex(3)(lin)(n,　K-2,t(+))　=　(1　+　o(t)(1))　1/6　root　t　-　1　.　n(3/2),　which　is　an　improvement　of　Gerbner,　Methuku　and　Vizer＇s　result　(Gerbner　et　al.,　2019).　Moreover,　we　also　prove　some　sharp　bounds　for　the　linear　Turan　number　of　K-s,t(+).　(C)　2020　Elsevier　Ltd.　All　rights　reserved.