As the only entry/exit for passengers getting on and off a train, the train plug door is of great importance to keep train operation safe and reliable. As signal processing technologies develop rapidly, taking the easy acquisition advantages of sound signals, a novel fault diagnosis method for train plug doors using multi-scale normalized permutation entropy (MNPE) and an improved particle swarm optimization based multi-class support vector machine (IPSO-MSVM) is proposed. Firstly, sound samples are collected using high-precision audio sensor. In the features extraction process, a hybrid method blending empirical mode decomposition (EMD), multi-scale permutation entropy (MNPE) with Fisher discrimination criterion is utilized. First, EMD is used to decompose each sound signal into several intrinsic mode functions (IMFs) and a residue for stationary processing. Then, MNPE features are extracted from the IMFs. To obtain the most significant features, the Fisher discrimination criterion is further applied. To address the time-consuming defects of traditional grid based method for selecting the optimal parameters of multi-class SVM, an improved PSO (IPSO) is proposed. The superiority of the IPSO-MSVM model and the hybrid feature extraction method was tested on the collected sound samples by comparing to commonly applied methods. Results indicate the identification accuracy of the proposed method is highest, which reaches 90.54%, demonstrating its feasibility.