In order to better identification the degradation state of bearing, a degradation state feature extraction method for bearing named LCD-Hilbert relative spectrum entropy is proposed based on 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 LCD-Hilbert relative frequency energy spectrum entropy（LHFE）, relative instantaneous energy spectrum entropy（LHIE） and relative singular spectrum entropy（LHSE） used as degradation feature. The degradation feature vector is composed of the three features. The practical vibration of bearing with inner race fault and outer race fault which in different degradation state are analyzed, and the support vector machine is further used to identification degradation state and the results demonstrate the ability of the proposed method.