Gas-insulated switchgear (GIS) is widely used in high-voltage power transmission systems. There has also been increasing demand for the real-time and online detection of faults in GIS equipment. In this study, a new type of optical fiber acoustic emission (AE) sensor based on the photoelastic effect and the polarization modulation method is proposed and fabricated. Partial discharge (PD)-induced AE signals of different defects were collected by this sensor and used for back-propagation artificial neural network (BP-ANN) training and recognition after data preprocessing and feature extraction. The results of the research show that a BP-ANN with self-adaptation and self-learning combined with the proposed sensor has good performance in the recognition and prediction of PD faults in GIS equipment, and the average accuracy of the test set reached 93.7%. The detection technology for weak AE signals and the fault identification method reported in this study can provide a reference for online monitoring of GIS and other equipment, which will have appreciable economic value and social significance.