There is an issue of low accuracy in deep learning-based fault identification methods for power distribution networks in conditions of insufficient measurements and low labeling rates. Thus a unified identification method of fault section and type is proposed based on graph semi-supervised and multi-task learning. First, a neural network architecture is designed for unified identification of fault section and type. This architecture integrates network topology and line parameter information into the graph embedding layer to effectively extract features of faults at different locations and types. Secondly, the fault section location and type identification tasks are constructed using a multi-task attention network. This is to extract multiple pieces of fault information and enable knowledge transfer between different tasks. Thirdly, graph embedding features and encoded compressed features of unlabeled samples are integrated to obtain new multi-task shared features, such that unlabeled samples can be fully used and the model’s generalizability can be enhanced. Finally, case studies demonstrate that the proposed method surpasses traditional neural networks in fault identification accuracy and shows better robustness in conditions of insufficient real-time measurements, low labeling rates and various types of measurement noise.