Aiming at the non-stationary time-varying characteristics of rolling bearing fault signals, a fault diagnosis method for rolling bearings was proposed, which integrates complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN), singular value decomposition(SVD) and cepstrum. By using CEEMDAN method, fault signals of rolling bearings are decomposed into a series of mode components, the correlation coefficient between each mode component and the fault signal of rolling bearing is calculated, and the threshold value of the correlation coefficient is set. The mode components whose correlation coefficients are smaller than the threshold value are eliminated by putting them into the last mode component as the trend component. The mode components obtained by the CEEMDAN method still contain noise, and the de-noising of each mode component is processed by SVD, and then the cepstrum analysis of each de-noised mode component is carried out to extract the fault characteristic frequencies of rolling bearings. The analysis results show that the cepstrum of each mode component decomposed by CEEMDAN method and de-noised by SVD can effectively extract the fault characteristic frequencies of different faults of rolling bearings such as inner ring fault, outer ring fault and ball fault. Thus, the effective diagnosis of different faults of rolling bearings can be realized.