In industry, sensor-based monitoring of equipment or environment has become a necessity. Instead of using a single sensor, multi-sensor system is used to fully detect abnormalities in complex scenarios. Recently, physical models, signal processing technology, and various machine learning models have improved the performance. However, these methods either do not consider the potential correlation between features or do not take advantage of the sequential changes of correlation while constructing an anomaly detection model. This paper firstly analyzes the correlation characteristic of a multi-sensor system, which shows a lot of clues to the anomaly/fault propagation. Then, a multi-sensor anomaly detection method, which finds and uses the correlation between features contained in the multidimensional time-series data, is proposed. The method converts the multidimensional time-series data into temporal correlation graphs according to time window. By transforming time-series data into graph structure, the task of anomaly detection is considered as a graph classification problem. Moreover, based on the stability and dynamics of the correlation between features, a structure-sensitive graph neural network is used to establish the anomaly detection model, which is used to discover anomalies from multi-sensor system. Experiments on three real-world industrial multi-sensor systems with anomalies indicate that the method obtained better performance than baseline methods, with the mean value of F1 score reaching more than 0.90 and the mean value of AUC score reaching more than 0.95. That is, the method can effectively detect anomalies of multidimensional time series.