In this article, we main study the uniqueness problem of meromorphic function which difference polynomials sharing common values. We consider the entire function $(f^n(f^m-1)prod_{j=1}^ {s}f(z+c_j)^{mu_j})^{(k)}$ and the meromorphic function $f^n(f^m-1)prod_{j=1}^{s}f(z+c_j)^{mu_j}$ to get the main results which extend Theorem 1.1 in paper[5] and theorem 1.4 in paper[6].

Keywords: meromorphic functions, difference , polynomials, uniqueness, sharing common value