The rapid development of smart factories, combined with the increasing complexity of production equipment, has resulted in a large number of multivariate time series that can be recorded using sensors during the manufacturing process. The anomalous patterns of industrial production may be hidden by these time series. Previous LSTM-based and machine-learning-based approaches have made fruitful progress in anomaly detection. However, these multivariate time series anomaly detection algorithms do not take into account the correlation and time dependence between the sequences. In this study, we proposed a new algorithm framework, namely, graph attention network and temporal convolutional network for multivariate time series anomaly detection (GTAD), to address this problem. Specifically, we first utilized temporal convolutional networks, including causal convolution and dilated convolution, to capture temporal dependencies, and then used graph neural networks to obtain correlations between sensors. Finally, we conducted sufficient experiments on three public benchmark datasets, and the results showed that the proposed method outperformed the baseline method, achieving detection results with F1 scores higher than 95% on all datasets.