Detecting rumors on social media has become particular important due to the rapid dissemination and adverse impacts on our lives. Though a set of rumor detection models have exploited the message propagation structural or temporal information, they seldom model them altogether to enjoy the best of both worlds. Moreover, the dynamics of knowledge information associated with the comments are not involved, either. To this end, we propose a novel Dual-Dynamic Graph Convolutional Networks, termed as DDGCN, which can model the dynamics of messages in propagation as well as the dynamics of the background knowledge from Knowledge graphs in one unified framework. Specifically, two Graph Convolutional Networks are adopted to capture the above two types of structure information at different time stages, which are then combined with a temporal fusing unit. This allows for learning the dynamic event representations in a more fine-grained manner, and incrementally aggregating them to capture the cascading effect for better rumor detection. Extensive experiments on two public real-world datasets demonstrate that our proposal yields significant improvements compared to strong baselines and can detect rumors at early stages.