In order to improve the effectiveness of fault feature extraction about rolling elements bearings and the accuracy of the transmission from time domain to angle domain in analysis of fault diagnosis, the research on the resample and the error analysis based on Lagrange transform was implemented. By combining resample that can switch time domain to angle domain with remainder formula for Lagrange interpolation and comparing remainder error with the theoretical error, the Lagrange resample based method that is high precision and small workload could be obtained. Finally the envelope spectrum from resample was compared with the one of original vibration signal. The results show that the fault feature of the envelope spectrum of angle domine signal is extracted easily, which verifies the method is effective.