Abstract: In order to meet the design requirements of improving the lightweight of the fixture under the condition of meeting the strength, a lightweight design method of the fixture based on the combination of numerical optimization and finite element simulation is proposed. Taking the geometric dimension of the jaw as the design variable, the minimization of the box mass as the optimization objective, and the strength and size as the constraint conditions, the mathematical model of the box lightweight optimization was established. Fifteen groups of numerical simulation test combinations were obtained by using Box Behnken test design, polynomial response surface approximation model was obtained by using multiple regression analysis fitting, and was introduced into the lightweight optimization mathematical model for iterative optimization. The results showed that the jaw mass of the optimized scheme was reduced by 32.3 % compared with the original scheme. The correctness of the optimization results is verified by the actual insulator replacement test.