Based on the improvement of threshold denoising method of morphological component analysis (MCA), a new method for the fault diagnosis of rolling bearings based on MCA is proposed. According to the morphological difference of each component, different sparse dictionaries are built by MCA to separate each component from the signal. When a rolling bearing is locally damaged, its vibration signal is often composed of harmonic component with system characteristics of the rolling bearing，impulse component with fault information and random noise. The harmonic component represents the smooth part of the vibration signal, while the impulse component represents the detail part of the vibration signal, therefore, the two kinds of components can be separated according to the morphological difference. The harmonic component, impulse component and random noise component are separated from the vibration signal of a fault rolling bearing by using the MCA, and the fault diagnosis of rolling bearing is carried out according to the time interval of impulses in the impulse component. The simulation and application examples have proved that the proposed method is effective in extracting the fault impulse component from the vibration signal of a local damaged rolling bearing.