bilevel optimization problem is a two-level optimization problem, where a subset of its variables is constrained in the optimizer set of another optimization problem parameterized by the remaining variables. in this talk, we introduce a lagrange multiplier expression method for bilevel polynomial optimization based on polynomial optimization relaxations. each relaxation is obtained from the kurash-kuhn-tucker (kkt) conditions for the lower level optimization and the exchange technique for semi-infinite programming. the global convergence of the method is proved under some general assumptions. and some numerical examples will be given to show the efficiency of the method.