Finding candidate molecules with favorable pharmacological activity, low toxicity, and proper pharmacokinetic properties is an important task in drug discovery. Deep neural networks have made impressive progress in accelerating and improving drug discovery. However, these techniques rely on a large amount of label data to form accurate predictions of molecular properties. At each stage of the drug discovery pipeline, usually, only a few biological data of candidate molecules and derivatives are available, indicating that the application of deep neural networks for low-data drug discovery is still a formidable challenge. Here, we propose a meta learning architecture with graph attention network, Meta-GAT, to predict molecular properties in low-data drug discovery. The GAT captures the local effects of atomic groups at the atom level through the triple attentional mechanism and implicitly captures the interactions between different atomic groups at the molecular level. GAT is used to perceive molecular chemical environment and connectivity, thereby effectively reducing sample complexity. Meta-GAT further develops a meta learning strategy based on bilevel optimization, which transfers meta knowledge from other attribute prediction tasks to low-data target tasks. In summary, our work demonstrates how meta learning can reduce the amount of data required to make meaningful predictions of molecules in low-data scenarios. Meta learning is likely to become the new learning paradigm in low-data drug discovery. The source code is publicly available at: https://github.com/lol88/Meta-GAT.