In the case of limited energy, the waste of energy and economic loss caused by abnormal electricity consumption should not be underestimated and its detection plays an important role. However, abnormal electricity consumption detection also faces many challenges. On the one hand, labeled abnormal data are difficult to obtain. On the other hand, building different models for different users undoubtedly increases the demand for data and the burden of training. To tackle these challenges, in this paper, we propose a transfer learning based graph convolutional network with self-attention mechanism method to detect abnormal electricity consumption. With the help of transfer learning, we firstly pre-train the source domain network using the sufficient data. Then, a small amount of data in the target domain is utilized to fine-tune the pre-training model to get the final detection model. This can not only effectively alleviate the problem of insufficient data, but also reduce the training burden caused by building different models for different users. In addition, to improve the effect of feature extraction and enhance the performance of the network, we employ the self-attention mechanism to enhance the network’s attention to different data information. Finally, we adopt the graph convolutional networks to discover the relationships of electricity consumption data among different moments and to classify the electricity consumption data. We have done detailed experiments to verify the effectiveness of the proposed method, and experimental results show that the proposed method is effective and robust.