Multi-task learning for molecular property prediction is becoming increasingly important in drug discovery. However, in contrast to other domains, the performance of multi-task learning in drug discovery is still not satisfying as the number of labeled data for each task is too limited, which calls for additional data to complement the data scarcity. In this paper, we study multi-task learning for molecular property prediction in a novel setting, where a relation graph between tasks is available. We first construct a dataset including around 400 tasks as well as a task relation graph. Then to better utilize such relation graph, we propose a method called SGNN-EBM to systematically investigate the structured task modeling from two perspectives. (1) In the \emph{latent} space, we model the task representations by applying a state graph neural network (SGNN) on the relation graph. (2) In the \emph{output} space, we employ structured prediction with the energy-based model (EBM), which can be efficiently trained through noise-contrastive estimation (NCE) approach. Empirical results justify the effectiveness of SGNN-EBM. Code is available on https://github.com/chao1224/SGNN-EBM.