Localized damage of rolling element bearings generates periodic impulses during running. The repeating frequency of impulses is a key indicator for diagnosing the localized damage of bearings. A new method, called Teager energy spectrum, is proposed to diagnose the faults of rolling element bearings. It exploits the unique advantages of Teager energy operator in detecting transient components in signals to extract periodic impulses of bearing faults, and uses the Fourier spectrum of Teager energy to identify the characteristic frequency of bearing faults. The effectiveness of the proposed method is validated by analyzing the experimental bearing vibration signals.