Abstract: In this paper we consider a property of claw-free graphs. We show that if d(u)+ d(v)≥ν(G)+2k+3, for every two nonadjacent vertices u and v, then G is 2k-vertex-deletable IM-extendable, where ν(G)=|V(G)|. And the bound is tight.

Key words: IM-extendable, vertex-deletable IM-extendable, claw-free graph