An approach based on kth-order cyclic moment was presented to deal with the fault feature extracting of the rolling bearing in incipient fault diagnosis. Firstly，based on cyclic statistics theory, the demodulation characteristics of the kth-order cyclic moment for time-varying amplitude modulation signal was studied, and the frequency characteristics were discussed. It was pointed out thatn kth-order cyclic moment could demodulate out the modulation frequency information , and obtain the carrier wave frequency information, and then the calculation m ethods were given. The analysis of the simulated signal demonstrates that the kth-order cyclic moment has quite good demodulation ability. An expermental investigation was performed to enable an assessment of the accuracy level . The result shows that the method based on kth-order cyclic moment has excellent reliability to early recognition of bearing failure.