With the digital transformation of the grid, partial discharge (PD) recognition using deep learning (DL) and big data has become essential for intelligent transformer upgrades. However, labeling on-site PD data poses challenges, even necessitating the removal of covers for internal examination, which makes it difficult to train DL models. To reduce the reliance of DL models on labeled PD data, this study proposes a semi-supervised approach for PD fault recognition by combining the graph convolutional network (GCN) and virtual adversarial training (VAT). The approach introduces a novel PD graph signal to effectively utilize phase-resolved partial discharge (PRPD) information by integrating numerical data and region correlations of PRPD. Then, GCN autonomously extracts features from PD graph signals and identifies fault types, while VAT learns from unlabeled PD samples and improves the robustness during training. The approach is validated using test and on-site data. The results show that the approach significantly reduces the demand for labeled samples and that its PD recognition rates have increased by 6.14% to 14.72% compared with traditional approaches, which helps to reduce the time and labor costs of manually labeling on-site PD faults.