When refiner gearbox has incipient failure,its vibration signal,with hidden impulse component veiled by strong background noise,is usually very weak,which results in difficultly of gear fault diagnosis. In this paper,the concept of M-shift correlated kurtosis( K,C,M,) was introduced,and the method of maximum correlated kurtosis deconvolution（ MCKD） was derived.Firstly,estimate interest period T of deconvolution through calculating the maximum K,C,M,value for the faulty signal. Then,select the appropriate M-shift for the maximum correlated kurtosis deconvolution. Finally,through envelope demodulation analysis to the MCKD filtered signal,the fault feature of root slight crack from gear 8（ Z,8,= 28） on the shaft V was successfully extracted. In addition,the MCKD method was compared to the method of fast spectral kurtosis. The application result and comparison analysis verify the effectiveness of the method of maximum correlated kurtosis deconvolution（ MCKD） applied to incipient fault diagnosis of gearbox.