Focusing on the difficulty of the combination optimization of modal from transmission system and vibration from structure system,taking the vertical mill reducer gearbox structural system geometrical parameter and transmission system parameter as design variables,to avoid the nature frequency and specific frequency overlapped and minimum the vibration of the reducer gearbox as the objective function,the volume,Von Mises stress and comprehensive displacement of the reducer gearbox as constraint condition,based on the multi- objective optimization theory,the weigh- adding of modal and vibration optimization is carried out. The modal- vibration combined optimization finite element model is built,the model is solved by using zero- order and first- order optimization methods. The optimization results indicate that the gap of nature frequency and specific frequency is reached at 20. 7%,and the vibration is attenuated by 28. 4%,the effective results is found for the combined optimization,which can provide method for multi- objective optimization and significant reference for practical issues of vibration and noise reduction.