Vibration analysis is an important means of monitoring gear condition and fault diagnosis. This work begins with the analysis of the characteristics of the correlation function. It was found through the theoretical analysis that the auto-correlation function does not change the modulation characteristics of the modulated signal, but has a significant noise reduction characteristic. In this way, the delay correlation demodulation method for the diagnosis of gear vibration failure is established. The stages of implementation of this method are as follows: the first stage is the auto-correlation analysis of measured vibration signals; The second is the delay of the auto-correlation function; the final step is the Hilbert demodulation transformation of the delayed auto-correlation function.