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Bilevel programming, a tool for modelling decentralized decisions, consists of the objectives of the upper level and lower level. And numerous methods are proposed for solving this problem. In this paper, we provide a genetic algorithm method for solving the linear bilevel programming. In our algorithm, we adopted some techniques to guarantee the not only the initial chromosomes but also the chromosomes generated by genetic operators are all feasible, which greatly reduces the searching space and avoiding the difficulty to deal with the infeasible points. Furthermore, it also enhances the efficiency of the algorithm that the best offsprings are selected to replace the parents in operator procedures. Some examples are illustrative to show the feasibility and efficiency of the algorithm proposed in this paper.