Abstract: Rumor detection has aroused increasing attention due to the damage caused by rampant rumors. Recent studies leverage the post content and propagation structure to detect rumors based on deep-learning based models. However, most of them focus on explicit interactions between posts in the spreading process, while ignoring the modeling of implicit relations, which limits the ability to encode the propagation structure. For example, in the interactive pattern of forwarding (commenting), there are often local implicit interactions between multiple forwarded (commented) posts. In this paper, we propose a rumor detection approach based on a multi-relational propagation tree, investigating multiple kinds of dependencies between posts and enhancing the influence of important posts, to capture richer propagation patterns. Specifically, we formulate the textual content and the propagation tree structure as a heterogeneous graph. Then, we present a novel multi-relational graph convolutional network to learn the inter-level dependency between parent and child nodes and the intra-level dependency between sibling nodes. Meanwhile, we exploit the source post and key spreading posts to model the potential influence of important posts in the spreading process. Finally, we aggregate the node features to learn a more discriminative representation for rumor detection. Extensive experiments on three public benchmark datasets demonstrate the effectiveness and superiority of our proposed method.