Spiral bevel gear is a basic transmission component and widely used in mechanical equipment， so it is important to monitor and diagnose its running state to ensure a safe operation. However， the vibration signals of spiral bevel gears are extremely complicated because of the changing number of meshing gear pairs， the position of meshing point and the transmission ratio， and the collisions between teeth during the meshing process. Especially， when the fault occurs， the vibration signals of spiral bevel gears present highly non-linear and non-stationary. This paper proposes a method for identifying the spiral bevel gear fault by using complete ensemble empirical mode decomposition with adaptive noise （CEEMDAN） permutation entropy as the sensitive features and support vector machines （SVMs） as the classifier. Firstly， the vibration signal is decomposed using CEEMDAN to obtain a series of internal modal functions （IMF） from a high frequency to a low frequency. The effective IMF components are optimized based on the correlation coefficient of each IMF component and the original signal， combining with the signal to noise ratio. Then， the permutation entropy values of the optimized IMFs are calculated. In order to obtain accuracy permutation entropy values， the overlapping parameter method is used to optimize the key parameters embedding dimension and delay time in the process of permutation entropy calculation. The eigenvectors are composed of the entropy values of the optimal IMFs， and the multi-class SVM is trained to identify the spiral bevel gear faults. The CEEMDAN permutation entropy method is applied to fault diagnosis of spiral bevel gears with three different fault states， and comparing with the method of EEMD permutation entropy and EMD permutation entropy. The results show that the fault diagnosis method based on CEEMDAN permutation entropy has a higher identification accuracy.