The topology of a modular multilevel converter is complex. When different phase sub modules fail, the traditional diagnosis method only detects the fault of a single sub module and cannot identify the multi-phase sub module fault. A multi class correlation vector machine algorithm is proposed for multi-phase fault diagnosis of a modular multilevel converter. The time-frequency data of three-phase voltage are transformed by Fourier transform to obtain the frequency domain data of the voltage. The typical low-order harmonic components in the frequency domain are used as the fault feature, and the multi classification correlation vector machine algorithm is used for fault classification. Through simulation of comparison with the traditional fault diagnosis method, the effectiveness and accuracy of the method are verified. The simulation results show that the proposed method is superior to the traditional fault diagnosis methods in training and testing accuracy. The training accuracy reaches 99.2%, and the test accuracy reaches 99.4%. It has a certain application value. This work is supported by the Science and Technology Project of State Grid Corporation of China (No. 52130416001Z).