Social Media Popularity Prediction has drawn a lot of attention because of its profound impact on many different applications, such as recommendation systems and multimedia advertising. Despite recent efforts to leverage the content of social media posts to improve prediction accuracy, many existing models fail to fully exploit the multiple dependencies between posts, which are important to comprehensively extract content information from posts. To tackle this problem, we propose a novel prediction framework named Dependency-aware Sequence Network (DSN) that exploits both intra- and inter-post dependencies. For intra-post dependency, DSN adopts a multimodal feature extractor with an efficient fine-tuning strategy to obtain task-specific representations from images and textual information of posts. For inter-post dependency, DSN uses a hierarchical information propagation method to learn category representations that could better describe the difference between posts. DSN also exploits recurrent networks with a series of gating layers for more flexible local temporal processing abilities and multi-head attention for long-term dependencies. The experimental results on the Social Media Popularity Dataset demonstrate the superiority of our method compared to existing state-of-the-art models.