Periodic impulses in vibration signals and its repeating frequency are the key indicators for diagnosing the local damage of rolling element bearings. A new method based on ensemble empirical mode decomposition (EEMD) and the Teager energy operator is proposed to extract the characteristic frequency of bearing fault. The signal is firstly decomposed into monocomponents by means of EEMD to satisfy the monocomponent requirement by the Teager energy operator. Then, the intrinsic mode function (IMF) of interest is selected according to its correlation with the original signal and its kurtosis. Next, the Teager energy operator is applied to the selected IMF to detect fault-induced impulses. Finally, Fourier transform is applied to the obtained Teager energy series to identify the repeating frequency of fault-induced periodic impulses and thereby to diagnose bearing faults. The principle of the method is illustrated by the analyses of simulated bearing vibration signals. Its effectiveness in extracting the characteristic frequency of bearing faults, and especially its performance in identifying the symptoms of weak and compound faults, are validated by the experimental signal analyses of both seeded fault experiments and a run-to-failure test. Comparison studies show its better performance than, or complements to, the traditional spectral analysis and the squared envelope spectral analysis methods.