Multivariate time series anomaly detection (MTAD) plays a vital role in a wide variety of real-world application domains. Over the past few years, MTAD has attracted rapidly increasing attention from both academia and industry. Many deep learning and graph learning models have been developed for effective anomaly detection in multivariate time series data, which enable advanced applications such as smart surveillance and risk management with unprecedented capabilities. Nevertheless, MTAD is facing critical challenges deriving from the dependencies among sensors and variables, which often change over time. To address this issue, we propose a coupled attentionbased neural network framework (CAN) for anomaly detection in multivariate time series data featuring dynamic variable relationships. We combine adaptive graph learning methods with graph attention to generate a global-local graph that can represent both global correlations and dynamic local correlations among sensors. To capture inter-sensor relationships and temporal dependencies, a convolutional neural network based on the global-local graph is integrated with a temporal self-attention module to construct a coupled attention module. In addition, we develop a multilevel encoder-decoder architecture that accommodates reconstruction and prediction tasks to better characterize multivariate time series data. Extensive experiments on real-world datasets have been conducted to evaluate the performance of the proposed CAN approach, and the results show that CAN significantly outperforms state-of-the-art baselines.