In recent years, deep learning has been successfully used in order to classify partial discharges (PDs) for assessing the condition of insulation systems in different electrical equipment. However, fault diagnosis using deep learning is still challenging, as it requires a large amount of training data, which is difficult and expensive to obtain in the real world. This paper proposes a novel one-shot learning method for fault diagnosis using a small dataset of phase-resolved PDs (PRPDs) in a gas-insulated switchgear (GIS). The proposed method is based on a Siamese network framework, which employs a distance metric function for predicting sample pairs from the same PRPD class or different PRPD classes. Experimental results over the small PRPD dataset that was obtained from an ultra-high-frequency sensor in the GIS show that the proposed method achieves outstanding performance for PRPD fault diagnosis as compared with the previous methods.