In order to solve the problem that the iterative process is prone to local oscillation and the algorithm is inefficient in the traditional BESO method, an improved BESO method based on weighted geometric mean iteration is proposed.By studying the influence degree of the current historical iterative step sensitivity weighting factor on the structural optimization process, and the iterative history change trend corresponding to the current iterative step sensitivity weighting factor, the optimal selection of current iterative step sensitivity weight is realized.It has been verified by three classical examples.Compared with the original filtering method and the filtering method based on arithmetic mean, the method presented can reduce the oscillation degree of the iterative process while maintaining the same stiffness, and significantly improve the stability of the iteration.The number of iterations is reduced, and the efficiency is increased by 10%—37.5%, which illustrates the feasibility and effectiveness of the method.