This study deals with the discrete optimization problem for the least steel structure weight, with member sections selected from available list. A method called Weight-Limited GA(Genetic Algorithm) is proposed to improve the traditional GA, with the crossover under a given limit to the weight of the best combination of previous generation. 10-bar, 11-bar and 17-bar plane trusses and 3-bay 5-story, 2-bay 8-story and 3-bay 12-story plane frames are taken as examples. Exact solutions of them are obtained by enumeration algorithm. GA and proposed method are performed on these examples simultaneously. Results have shown that the proposed method is valid in improving the convergence rate and actuate ratio.