Graph anomaly detection, a crucial task in data mining, holds significant application potential in diverse domains such as biology and finance. However, existing methods fail to sufficiently capture both global and local dependencies of anomalous nodes in graph anomaly detection tasks. To address this limitation, we propose a novel method, GLDAD, that explicitly decouples global and local dependencies for anomaly detection in graphs. Specifically, to improve the anomaly detection capability in graph data, we introduce an innovative model that efficiently disentangles the complex global and local dependencies among graph nodes. To capture global dependency, we design a global anomaly-aware module that captures the global relationships of anomalous nodes using a self-attention mechanism. Furthermore, we introduce a local anomaly-aware module that retains the feature information of local nodes by concatenating low-order neighborhood features and performing low-dimensional mapping, thereby effectively modeling the local dependencies of anomalous nodes. Experimental results on three real world datasets demonstrate that GLDAD outperforms various baseline methods, achieving substantial improvements in graph anomaly detection performance.