Current document-level neural machine translation (NMT) systems have achieved remarkable progress with document context. Nevertheless, discourse information that has been proven effective in many NLP tasks is ignored in most previous work. In this work, we aim at incorporating the coherence information hidden within the RST-style discourse structure into machine translation. To achieve it, we propose a document-level NMT system enhanced with the discourse-aware document context, which is named Disco2NMT. Specifically, Disco2NMT models document context based on the discourse dependency structures through a hierarchical architecture. We first convert the RST tree of an article into a dependency structure and then build the graph convolutional network (GCN) upon the segmented EDUs under the guidance of RST dependencies to capture the discourse-aware context for NMT incorporation. We conduct experiments on the document-level English-German and English-Chinese translation tasks with three domains (TED, News, and Europarl). Experimental results show that our Disco2NMT model significantly surpasses both context-agnostic and context-aware baseline systems on multiple evaluation indicators.