An　r-uniform　hypergraph　is　linear　if　every　two　edges　intersect　in　at　most　one　vertex.　Let　Kr+1　be　a　complete　graph　with　r　+　1　vertices.　The　r-uniform　hypergraph　K-r+1(+),　is　obtained　from　Kr+1　by　enlarging　each　edge　of　Kr+1　with　r　-　2　new　vertices　disjoint　from　V(Kr+1)　such　that　distinct　edges　of　Kr+1　are　enlarged　by　distinct　vertices.　Let　H　be　a　K-r+1(+)-free　linear　r-uniform　hypergraph　with　n　vertices.　In　this　paper,　we　prove　that　when　n　is　sufficiently　large,　the　spectral　radius　rho(H)　of　the　adjacency　tensor　of　H　is　no　more　than　n/r,　i.e.,　rho(H)　＜=　n/r　with　equality　if　and　only　if　r　vertical　bar　n　and　H　is　a　transversal　design,　where　the　transversal　design　is　the　balanced　r-partite　r-uniform　hypergraph　such　that　each　pair　of　vertices　from　distinct　parts　is　contained　in　one　hyperedge　exactly.　An　immediate　corollary　of　this　result　is　that　ex(r)(lin)　(n,　K-r+1(+))　=　n(2)/r(2)　for　sufficiently　large　n　and　r　vertical　bar　n,　where　ex(r)(lin)　(n,　K-r+1(+))　is　the　maximum　number　of　edges　of　an　n-vertex　K-r+1(+)-free　linear　r-uniform　hypergraph,　i.e.,　the　linear　Turan　number　of　K-r+1(+).