The recent success of deep learning has significantly boosted molecular property prediction, advancing therapeutic activities such as drug discovery. The existing deep neural network methods usually require sufficient training data for each property, impairing their performances over cases (especially for new molecular properties) with a limited amount of laboratory data which are common in real situations. To this end, we propose Meta-MGNN, a novel model for few- shot molecular property prediction. Meta-MGNN applies molecular graph neural networks to learn molecular representation and builds a meta-learning framework for model optimization. To exploit unlabeled molecular information and address task heterogeneity of different molecular properties, Meta-MGNN further incorporates molecular structure and attribute based self-supervised module and self-attentive task weight into the former framework, strengthening the whole learning model. Extensive experiments on two public multi-property datasets demonstrate that Meta-MGNN outperforms a variety of state-of-the-art methods.