Multivariate time series anomaly detection is a challenging task due to the intricate intra- and inter-metric dependencies present in the data. Previous methods have mainly focused on capturing intra-metric dependency, while neglecting the utilization of the dependency information across metrics. More recent approaches have considered inter-metric dependency, but have not been able to capture the complex inter-metric dynamics accurately and adaptively. To address these challenges, we propose a novel dual-attentional multivari-ate time series anomaly detection framework. Our approach improves on the original Dot-Product Attention to robustly capture intra-metric dependency. Additionally, we introduce automatic graph structure learning and graph attention mechanism to adaptively capture inter-metric dependency and utilize it effectively. Experiments on five public datasets from different domains demonstrate that comprehensive and accurate modeling of both dependencies enables our proposed method to outperform baseline methods in accurately detecting anomalies.