A large number of sensors are typically installed in industrial plants to collect real-time operational data. These sensors monitor data with time series correlation and spatial correlation over time. In previous studies, GNN has built many successful models to deal with time series data, but most of these models have fixed perspectives and struggle to capture the dynamic correlations in time and space simultaneously. Therefore, this paper constructs a multi-scale dynamic graph neural network (MSDG) for anomaly detection in industrial sensor data. First, a multi-scale sliding window mechanism is proposed to input different scale sensor data into the corresponding network. Then, a dynamic graph neural network is constructed to capture the spatial–temporal dependencies of multivariate sensor data. Finally, the model comprehensively considers the extracted features for sequence reconstruction and utilizes the reconstruction errors for anomaly detection. Experiments have been conducted on three real public datasets, and the results show that the proposed method outperforms the mainstream methods.