The integrations of advanced metering infrastructure and smart meters make it possible to detect electricity thieves by analyzing electricity consumption readings. However, the detection accuracies of traditional models are limited due to their difficulty in capturing the periodicity and latent features from electricity consumption readings. To solve this problem, a graph attention network (GAT)-based model is proposed to improve the detection accuracy from a fresh viewpoint on graph domains. First, a new strategy is presented to transform raw one-dimensional electricity consumption readings into dynamic graphs, which represent the features and periodicity through feature matrices and correlation matrices, respectively. Then, a GAT is migrated from traditional graph inferences into electricity theft detection, in which necessary adjustments are made on structures to capture periodicity and latent features from dynamic graphs. Case studies show that the proposed model outperforms popular baselines for a wide range of training ratios and fraudulent ratios.