Rotating machinery is typical complex electromechanical equipment under nonstationary working conditions and hazardous environments, which is thus vulnerable to an unexpected fault. The currently wide-applied deep learning-based fault diagnosis methods for rotating machines require a huge amount of training data and can only extract features from independent samples. In this study, a semi-supervised self-correcting graph neural network (SSGNN) is proposed for fault diagnosis, which effectively extracts features from vibrational signals and generates a graph-structured representation of fault knowledge. First, a preprocessing layer is introduced to mine the propinquity of vibration samples and construct a graph, where circle loss is applied to enhance convergence. Second, the state transform algorithm is improved by proposing a graph convolutional layer for efficiently implementing state propagation. Finally, an alternate learning method is proposed based on the expectation maximization (EM) algorithm, in which the feature extraction network and graph structure are optimized alternately to reduce the training complexity. The proposed method is validated through experiments conducted on a publicly available dataset and a dynamic condition dataset obtained from a drivetrain dynamic simulator. The results show that the proposed method has higher accuracy and faster convergence speed compared to the state-of-the-art methods.