Finite element model of big arm of MD-1200YJ palletizing robot was established,the accuracy of the finite element model was verified by modal test.By static analysis taking into account dynamic factors, constrained modal analysis, vibration response test and frequency response analysis to determine to use minimal mass, maximizing the first and second natural frequency, minimizing the maximal stress, minimizing the maximal deformation and as the optimization objectives. Taking structure parameters as design variables and boundary conditionsof design variables as the constraint conditions, the approximation models of objective functions and constraint functions were established by the Box-Behnken and the RSM. The optimal solution was obtained by using NSGA-II algorithm. The results show that, in the case of the first two natural frequencies were increased, the structural stiffness and vibration stability were improved, the influence of vibration on fatigue damage of parts was reduced, meanwhile the maximum stress and deformation within allowable values range, the mass reduction was 11.3%. The validity of this lightweight design method was verified.