Graph anomaly detection (GAD) is increasingly crucial in various applications, ranging from financial fraud detection to fake news detection. However, current GAD methods largely overlook the fairness problem, which might result in discriminatory decisions skewed toward certain demographic groups defined on sensitive attributes (e.g., gender, religion, ethnicity, etc.). This greatly limits the applicability of these methods in real-world scenarios in light of societal and ethical restrictions. To address this critical gap, we make the first attempt to integrate fairness with utility in GAD decision-making. Specifically, we devise a novel DisEntangle-based FairnEss-aware aNomaly Detection framework on the attributed graph, named DEFEND. DEFEND first introduces disentanglement in GNNs to capture informative yet sensitive-irrelevant node representations, effectively reducing societal bias inherent in graph representation learning. Besides, to alleviate discriminatory bias in evaluating anomalous nodes, DEFEND adopts a reconstruction-based anomaly detection, which concentrates solely on node attributes without incorporating any graph structure. Additionally, given the inherent association between input and sensitive attributes, DEFEND constrains the correlation between the reconstruction error and the predicted sensitive attributes. Our empirical evaluations on real-world datasets reveal that DEFEND performs effectively in GAD and significantly enhances fairness compared to state-of-the-art baselines. To foster reproducibility, our code is available at https://github.com/AhaChang/DEFEND.