Graph anomaly detection (GAD), which aims to identify those graphs that are significantly different from other ones, has gained growing attention in many real-world scenarios. However, existing GAD methods are generally designed for centralized training, while in real-world collaboration, graph data is generally distributed across various clients and exhibits significant non-IID characteristics. To tackle this challenge, we propose a federated graph anomaly detection framework with local-global anomaly awareness (LG-FGAD). We first introduce a self-adversarial generation module and train a discriminator to identify the generated anomalous graphs from the normal graph. To enhance the anomaly awareness of the model, we propose to maximize/minimize the mutual information from local and global perspectives. Importantly, to alleviate the impact of non-IID problems in collaborative learning, we propose a dual knowledge distillation module. The knowledge distillation is conducted over both logits and embedding distributions, and only the student model engages in collaboration to preserve the personalization of each client. Empirical results on various types of real-world datasets prove the superiority of our method.