The classification of semisimple Lie algebras with involutions can be found in. The Hom-Lie algebras were initially introduced by Hartwig, Larson and Silvestrov in motivated initially by examples of deformed Lie algebras coming from twisted discretizations of vector fields. The Killing form K of g is nondegenerate and ˆ Iy&&is symmetric with respect to K. In, the author studied Hom-Lie triple system using the double extension and gives an inductive description of quadratic Hom-Lie triple system. In this work we recall the definition of involutive Hom-Lie triple systems and some related structure and we prove that all involutive Hom-Lie triple systems are whether simple or semi-simple. Moreover,we prove that an involutive simple Lie triple system give a rise of Involutive Hom-Lie triple system. A Hom-Lie triple system is a triple ( ,[ , , ], ) L −−− α consisting of a linear space L , a trilinear map [ , , ]: −−− × × → LLL L and a linear map α : L L → such that [, ,] 0 xyz = (skewsymmetry) [, ,] [,, ] [, , ] 0 xyz yzx zxy ++= (ternary Jacobi identity) [ ( ), ( ),[ , , ]] α α u v xyz =++ [[ , , ], ( ), ( )] [ ( ),[ , , ], ( )] [ ( ), ( ),[ , , ]], uvx y z x uvy z x y uvz αα α α αα for all xyzuv L ,,,, ε . If Moreover α satisfies α ααα ([ , , ]) [ ( ), ( ), ( )] xyz x y z = (resp. 2 L α = id ) for all xyz L , , ε , we say that ( ,[ , , ], ) L −−− α is a multiplicative (resp. involutive) HomLie triple system. A Hom-Lie triple system ( ,[ , , ], ) L −−− α is said to be regular if α is an automorhism of L .