In this paper, we will prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth: -Delta(p)u = vertical bar u vertical bar(p)*(-2)u + mu vertical bar u vertical bar(p-2)u in Omega, u =0 on partial derivative Omega, provided N > p(2) + p, where Delta(p) is the p-Laplacian operator, 1 < p < N, p* = pN/N-p, mu > 0 and Omega is an open bounded domain i...