Molecular property prediction plays a fundamental role in drug discovery to discover candidate molecules with target properties. However, molecular property prediction is essentially a few-shot problem which makes it hard to obtain regular models. In this paper, we propose a property-aware adaptive relation networks (PAR) for the few-shot molecular property prediction problem. In comparison to existing works, we leverage the facts that both substructures and relationships among molecules are different considering various molecular properties. Our PAR is compatible with existing graph-based molecular encoders, and are further equipped with the ability to obtain property-aware molecular embedding and model molecular relation graph adaptively. The resultant relation graph also facilitates effective label propagation within each task. Extensive experiments on benchmark molecular property prediction datasets show that our method consistently outperforms state-of-the-art methods and is able to obtain property-aware molecular embedding and model molecular relation graph properly.