The indicator of bearing degradation is one of the most important parts in the study of bearing. The effective indicators can help warn of degradation before bearing failure. In this paper,the entropy with time parameter is proposed as the degradation index. By introducing time parameter,the entropy based on wavelet packet transform is improved,and the Gaussian model is used to optimize the expression of the indicator. The data of run-to-failure is from FEMTO-ST Institute to verify the feasibility of the method. The experiment result shows that the indicator is less affected by the optional conditions. It can also characterize the degradation state under different working conditions and realize the early warning of bearing failure by calculating the its rate of change.