The vertex cover polynomial of a graph G of order n has been already introduced in [3]. It is defined as the polynomial, C (G, x) = c (G, i)xi , where C(G,i) is the number of vertex covering sets of G of size i and β (G) is the covering number of G. In this paper we have established a general formula for finding the vertex Cover Polynomial to the product of P2 with the complete graph Kn,(ie G=K_(1,n)×P_2). The coefficient of the polynomial satisfies some identities. Also we have proved that the coefficient of the vertex cover, polynomial C(G,x)is log-Concave.