In this paper, we study the uniqueness of entire functions and prove the following theorem. Let f be a transcendental entire function of finite order. Then there exists at most one positive integer k, such that  f ( z )∆ ^k _c f ( z ) −R ( z ) has finitely many zeros, where R ( z ) is a non-vanishing rational function and c is a nonzero complex number. Our result is an improvement of the theorem given by Andasmas and Latreuch [1].