Identifying power transformer faults accurately is critical to maintaining the stable operation of power system. Intelligent fault diagnosis algorithms based on dissolved gases have been extensively researched and implemented. However, in practice, collecting labeled data is time-consuming and costly. Therefore, it is necessary to establish a valid diagnostic model with limited labeled data. To solve this problem, a novel semi-supervised learning method for power transformer fault diagnosis is proposed in this paper. First, all the dissolved gas samples are constructed as a weighted K-nearest neighbor (KNN) graph to initially describe association among all samples. Then, a semi-supervised random multireceptive field propagation graph convolutional network (SSRMFPGCN) is designed for fault feature extraction and classification. Finally, the collected power transformer fault data are used to validate the proposed method. The experimental results show that the method proposed in this paper can still achieve 94.06% accuracy with only 20% of labeled training samples, which is significantly superior to the traditional intelligent diagnosis methods.