In this paper, we study bilevel mixed integer programming (MIP) problem and present a novel computing scheme based on reformulations and decomposition strategy. By converting bilevel MIP into a constrained mathematical program, we present its single-level reformulations that are friendly to perform analysis and build insights. Then, we develop a decomposition algorithm based on column-and-constraint generation method, which converges to the optimal value within nite operations. A preliminary computational study on randomly generated instances is presented, which demonstrates that the developed computing scheme has a superior capacity over existing methods. As it is generally applicable, easy-to-use and computationally strong, we believe that this solution method makes an important progress in solving challenging bilevel MIP problem.