Let G be a simple graph.G is called s-vertex connected if every induced subgraph with s vertices is connected but there exists an induced subgraph with s-1 vertices that is not connected

where s ≥ 3.A path P is extendable if there exists another path P′ such that V(P′)V(P) and |V(P′)|=|V(P)| + 1.A graph G is said to be fully path extendable if its diameter is at most two and every path P with |V(P)| < |V(G)| is extendable.In this paper

we prove that an s-vertex connected graph whose order is not less than 2s-1 is fully path extendable.