In order to better identification the degradation state of bearing, the degradation feature extraction method of bearing degradation state are studied. A degradation state feature extraction method for bearing named HHT relative spectrum entropy is proposed based on HHT for analyzing non-stationary vibration signal and relative entropy for characterizing the probability distribution difference among different signals. The analysis results of simulation signal demonstrate the availability and relationality of the proposed HHT relative energy spectrum entropy（HREE） and HHT relative singular spectrum entropy（HRQE） used as degradation feature. The degradation feature vector is composed of the two feature. The practical vibration of bearing with inner race fault and outer race fault which in different degradation state are analyzed, and the relevance vector machine is further used to identification degradation state and the results demonstrate the ability of the proposed method.