Graph anomaly detection plays a crucial role in identifying exceptional instances in graph data that deviate significantly from the majority. It has gained substantial attention in various domains of information security, including network intrusion, financial fraud, and malicious comments, et al. Existing methods are primarily developed in an unsupervised manner due to the challenge in obtaining labeled data. For lack of guidance from prior knowledge in unsupervised manner, the identified anomalies may prove to be data noise or individual data instances. In real-world scenarios, a limited batch of labeled anomalies can be captured, making it crucial to investigate the few-shot problem in graph anomaly detection. Taking advantage of this potential, we propose a novel few-shot Graph Anomaly Detection model called FMGAD (Few-shot Message-Enhanced Contrastive-based Graph Anomaly Detector). FMGAD leverages a self-supervised contrastive learning strategy within and across views to capture intrinsic and transferable structural representations. Furthermore, we propose the Deep-GNN message-enhanced reconstruction module, which extensively exploits the few-shot label information and enables long-range propagation to disseminate supervision signals to deeper unlabeled nodes. This module in turn assists in the training of self-supervised contrastive learning. Comprehensive experimental results on six real-world datasets demonstrate that FMGAD can achieve better performance than other state-of-the-art methods, regardless of artificially injected anomalies or domain-organic anomalies.