Automatically verifying rumorous information has become an important and challenging task in natural language processing and social media analytics. Previous studies reveal that people’s stances towards rumorous messages can provide indicative clues for identifying the veracity of rumors, and thus determining the stances of public reactions is a crucial preceding step for rumor veracity prediction. In this paper, we propose a hierarchical multi-task learning framework for jointly predicting rumor stance and veracity on Twitter, which consists of two components. The bottom component of our framework classifies the stances of tweets in a conversation discussing a rumor via modeling the structural property based on a novel graph convolutional network. The top component predicts the rumor veracity by exploiting the temporal dynamics of stance evolution. Experimental results on two benchmark datasets show that our method outperforms previous methods in both rumor stance classification and veracity prediction.