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Many multivariate time series anomaly detection frameworks have been proposed and widely applied. However, most of these frameworks do not consider intrinsic relationships between variables in multivariate time series data, thus ignoring the causal relationship among variables and degrading anomaly detection performance. This work proposes a novel framework called CGAD, an entropy Causal Graph for multivariate time series Anomaly Detection. CGAD utilizes transfer entropy to construct graph structures that unveil the underlying causal relationships among time series data. Weighted graph convolutional networks combined with causal convolutions are employed to model both the causal graph structures and the temporal patterns within multivariate time series data. Furthermore, CGAD applies anomaly scoring, leveraging median absolute deviation-based normalization to improve the robustness of the anomaly identification process. Extensive experiments demonstrate that CGAD outperforms state-of-the-art methods on real-world datasets with a 9% average improvement in terms of three different multivariate time series anomaly detection metrics.