Let G = (V (G), E(G)) be a graph with n vertices and for A graph which admits neighborhood-prime labeling is called a neighborhood-prime graph and if in a graph G, every vertex is of degree at most 1, then such a graph is neighborhood-prime vacuously. In this paper, we show that the generalized Petersen graph P (n, k) is neighborhood-prime when the greatest common divisor of n and k is 1, 2 or 4 and we also show that P (n, 8) is neighborhood-prime for all n.