Correntropy is an effective method to deal with Gaussian and non-Gaussian noise. Aiming at the problem of gear fault diagnosis under the interference of strong Gaussian noise and non-Gaussian noise，a gear fault diagnosis method based on correntropy and bi-spectrum is put forward. Gaussian kernel function and incomplete Cholesky decomposition algorithm are used to calculate the correntropy of the vibration signal，the bi-spectrum of the correntropy is calculated，and the gear fault is identified according to the bi-spectrum characteristics of the correntropy. The incomplete Cholesky decomposition based correntropy algorithm not only greatly reduces the amount of data，highlights the fault characteristics of the gear，but also improves the calculation efficiency. The results of simulation and vibration signal analysis of gear wear fault show that the strong background noise will cause the failure of the traditional bi-spectrum fault diagnosis method，while the gear fault diagnosis method based on correntropy and bi-spectrum analysis can extract the fault features of gear in the background of strong noise interference，accurately identify gear fault，and its performance is better than that of traditional bi-spectrum and wavelet transform domain bi-spectrum，which is an effective method for gear fault diagnosis.