To extract the weak periodic impulse characteristics of vibration signal measured from the rolling bearing when local defects occur, a fault diagnosis method of rolling bearings combining an optimal ensemble empirical mode decomposition (OEEMD) with Teager energy operator is proposed. The OEEMD method is presented to determine two critical parameters k (the amplitude coefficient of the added white noise) and m (the number of ensemble trials)of the ensemble empirical mode decomposition (EEMD). It combines the correlation coefficient, relative root-mean-square of the error (RRMSE) and signal-to-noise ratio to guide the selection of the two critical parameters. The impulse is separated from the vibration signals of a rolling bearing by OEEMD. Then, the instantaneous amplitude is estimated by Teager energy operator and the characteristic frequency of the impulse component can be acquired from the envelope spectrum of the instantaneous amplitude. In the end, the rolling bearing faults are diagnosed. Both the simulation and experimental data prove The effectiveness of the proposed method.