The prediction of molecular properties is a fundamental task in the field of drug discovery. Recently, Graph Neural Networks (GNNs) have been gaining prominence in this area. Since a molecule tends to have multiple correlated properties, there is a great need to develop the multi-task learning ability of GNNs. However, limited by expensive and time-consuming human annotations, collecting complete labels for each task is difficult. As a result, most existing benchmarks involve a lot of missing labels in training data, and the performance of GNNs is impaired for lacking enough supervision information. To overcome this obstacle, we propose to improve multi-task molecular property prediction via missing label imputation. Specifically, a bipartite graph is firstly introduced to model the molecule-task co-occurrence relationships. Then, the imputation of missing labels is transformed into predicting missing edges on this bipartite graph. To predict the missing edges, a graph neural network is devised, which can learn the complex molecule-task co-occurrence relationships. After that, we select reliable pseudo-labels according to the uncertainty of the prediction results. Boosting with enough and reliable supervision information, our approach achieves the state-of-the-art performance on a variety of real-world datasets.