Using the finite element software ANSYS Workbench, the static analysis of the clamping jaws of the exhaust pipe welding fixture clamping mechanism was carried out, and the deformation and stress distribution of the clamping jaws were obtained. On the premise that the gripper meets the strength and stiffness requirements of exhaust pipe welding, the size of the gripper is optimized by the response surface optimization method in multi-objective optimization. First, the mathematical model of gripper optimization is established, and the objective function and constraints are set. Conditions, and then parameterize each size of the gripper, and obtain the  coptimal design size of the gripper by calculation. The topological optimization of the jaw structure is then carried out by the variable density method to reduce its mass. Comparing the deformation and stress distribution before and after optimization of the clamping jaw the results show that the weight of the campina jaw is reduced by 27.9% when the stress and deformation meet the design requirements after the optimization.