Aiming at the problem that the traditional fault diagnosis method has a low efficiency for spiral bevel gear fault diagnosis, a fault diagnosis method based on local bispectrum and convolution neural network（CNN） is proposed. By using local bispectrum of spiral bevel gears vibration signal containing global information as the input of the CNN, a diagnosis model is constructed to realize fault diagnosis of spiral bevel gears, which not only reduces the redundancy of fault information, but also improves the speed of CNN training. Comparing with traditional diagnosis results that use bispectrum and CNN, vibration signal and CNN, local bispectrum and SVM（Support Vector Machine）, local bispectrum and BP（Back Propagation） neural network, the proposed method has an optimal comprehensive performance which has an accuracy of 99.56% and model training time of 15 seconds.