This paper presents a genetic algorithm method for solving convex quadratic bilevel programming problem. Bilevel programming problems arise when one optimization problem, the upper problem, is constrained by another optimization, the lower problem. In this paper, the bilevel convex quadratic problem is transformed into a single level problem by applying Kuhn-Tucker conditions, and then an efficient method based on genetic algorithm has been proposed for solving the transformed problem. By some rule, we simplify the transformed problem, so we can search the optimum solution in the feasible region, and reduce greatly the searching space. Numerical experiments on several literature problems show that the new algorithm is effective in practice.