This work aims to present a method of promoting the vibration performance of the gear and change the variation coefficient with respect to some unreasonable designs for gear of reduction gearbox in capper. Natural frequency and vibration mode were confirmed by modal analysis. 3D modeling was conducted by Solidworks with variation coefficient of spur gear as independent variable. Then Ansys Workbench was used to do modal analysis. At last, experiment data were imported into Matlab for analysis and polynomial fitting. The natural frequency of spur gear decreased with the increase of the variation coefficient and had a sudden change when the variation coefficient was zero. It decreased firstly and increased then in a small range with the increase of the variation coefficient. The change curves could be accurately fitted with ten fitting curves. In conclusion, the work can be used as a useful reference for the study of the natural frequency and vibration mode of gear and the optimization design of the reduction gearbox for capper.