Taking the headstock of 140 kN continuous drive friction welder as the research object, the static and dynamic characteristics of the spindle box were analyzed by using the finite element analysis software. In order to improve the comprehensive mechanical properties of the headstock and realize material rational use of the spindle box, the central composite experimental design was carried out with seven structural parameters such as the wall thickness of the box as design variables. According to the obtained data results, the response surface model of the spindle box was established based on Kriging interpolation method, and the sensitivity analysis of each design variable was carried out. The optimization design of the headstock was completed by using multiobjective genetic algorithm, the spindle box had a weight reduction of 16.6%, achieving a lightweight design of the welder. After verifying the fitting accuracy of the spindle box response surface model, it was verified that the combination of CCD experiment method and Kriging interpolation method could be used to effectively and accurately complete the establishment of the spindle box response surface model. Therefore, this optimization method can be applied to the design of other types of machine tool parts.