Molecular property prediction plays a fundamental role in drug discovery to identify candidate molecules with target properties. However, molecular property prediction is essentially a few-shot problem, which makes it hard to use regular machine learning models. In this paper, we propose Property-Aware Relation networks (PAR) to handle this problem. In comparison to existing works, we leverage the fact that both relevant substructures and relationships among molecules change across different molecular properties. We first introduce a property-aware embedding function to transform the generic molecular embeddings to substructure-aware space relevant to the target property. Further, we design an adaptive relation graph learning module to jointly estimate molecular relation graph and refine molecular embeddings w.r.t. the target property, such that the limited labels can be effectively propagated among similar molecules. We adopt a meta-learning strategy where the parameters are selectively updated within tasks in order to model generic and property-aware knowledge separately. Extensive experiments on benchmark molecular property prediction datasets show that PAR consistently outperforms existing methods and can obtain property-aware molecular embeddings and model molecular relation graph properly.