Let P be a simple polygon of n vertices. A set of points S in P is called a guard sufficient set of P if all guard set of P can also guard all points of S. Especially, if the set of all vertices V(P) in P is a guard sufficient set of P, P is called V-guard sufficient polygon(V-GSP). In this paper, we introduce some conditions for V-GSP and present efficient V-GSP decision algorithm with $O(n^2)$ time complexity and data structures for this algorithm.
