The shift invariant characteristic of tunable Qfactor wavelet transform (TQWT) was analyzed

and verified through simulated signal. A method named adaptive tunable Qfactor wavelet transform (ATQWT) based on timefrequency kurtosis index optimization was proposed to solve the problem of incipient fault diagnosis of rolling bearing. Firstly

the timefrequency kurtosis index was used to search for the quality factor and the redundancy factor of TQWT； after the optimal influencing parameters were confirmed

the parameters of TQWT were set according to the obtained results and the original signal was processed

then the corresponding signal components could be acquired and the optimal signal component could be confirmed. The envelope demodulation process was performed on the optimal signal component. Finally

the condition of the bearing could be judged by analyzing the frequency components of the envelope spectrum. The analysis results of the experiment signals show the timefrequency kurtosis index by the proposed method is more reliable

and robustrness is better. This method could accurately separate the weak feature from the original signal at low signal to noise ratio

and effectively judge the incipient fault of bearing.