In power electronic traction transformer, the failure of the single-phase PWM rectifier will lead to irreparable degradation of the system. Thus, this article proposes a feasible data-driven method to diagnose both the current sensor faults and insulated gate bipolar transistors (IGBTs) open-circuit faults of single-phase PWM rectifier online. The principle of the method is to construct a signal predictor by combining nonlinear autoregressive exogenous (NARX) model and an advanced learning algorithm, Extreme Learning Machine (ELM). Then the faults are detected based on the residual between the signal output of the predictor and the sensor. Furthermore, the faults are identified by logical judgment based on the system fault performance. Several hardware-in-loop tests are implemented to verify the applicability and effectiveness of the proposed diagnosis method. Test results show that this method has a very fast speed to detect the faults within 1 ms and a high accuracy to classify different faults.