In this paper, we study a uniqueness question of transcendental entire functions sharing two distinct rational functions IM with their k-th order derivatives. The main result obtained in this paper extends the corresponding result concerning non-constant entire functions sharing two distinct small functions IM with their first order derivatives, which was proved by Qiu Gangdi in 2000, and gives an affirmative answer to a conjecture proposed by Li Ping and Yang Chungchun in 1999 based upon the assunption that transcendental entire functions sharing two distinct rational functions IM with their k-th order derivatives.