This study proposes a new method of fault diagnosis based on the least squares support vector machine with gradient information (G-LS-SVM) to solve the insulated-gate bipolar transistor(IGBT) open-circuit failure problem of the traction inverter in a catenary power supply system. First, a simulation model based on traction inverter topology is built, and various voltage fault signal waveforms are simulated based on the IGBT inverter open-circuit fault classification. Second, compressive sensing theory is used to sparsely represent the voltage fault signal and make it a fault signal. The new method has a high degree of sparseness and builds an overcomplete dictionary model containing the feature vectors of voltage fault signals based on a double sparse dictionary model to match the sparse signal characteristics. Finally, the space vector transform is used to represent the three-phase voltage scalar in the traction inverter as a composite quantity to reduce the redundancy of the fault signals and data-processing capabilities. A G-LS-SVM fault diagnosis model is then built to diagnose and identify the voltage fault signal feature vector in an overcomplete dictionary. The simulation results show that the accuracy of this method for various types of IGBT tube fault diagnosis is over 98.92%. Moreover, the G-LS-SVM model is robust and not affected by Gaussian white noise.