Discourse relations between sentences are often represented as a tree, and the tree structure provides important information for summarizers to create a short and coherent summary. However, current neural network-based summarizers treat the source document as just a sequence of sentences and ignore the tree-like discourse structure inherent in the document. To incorporate the information of a discourse tree structure into the neural network-based summarizers, we propose a discourse-aware neural extractive summarizer which can explicitly take into account the discourse dependency tree structure of the source document. Our discourse-aware summarizer can jointly learn the discourse structure and the salience score of a sentence by using novel hierarchical attention modules, which can be trained on automatically parsed discourse dependency trees. Experimental results showed that our model achieved competitive or better performances against state-of-the-art models in terms of ROUGE scores on the DailyMail dataset. We further conducted manual evaluations. The results showed that our approach also gained the coherence of the output summaries.