Sequence-to-sequence methods have achieved promising results for textual abstractive meeting summarization. Different from documents like news and scientific papers, a meeting is naturally full of dialogue-specific structural information. However, previous works model a meeting in a sequential manner, while ignoring the rich structural information. In this paper, we develop a Dialogue Discourse-Aware Graph Convolutional Networks (DDA-GCN) for meeting summarization by utilizing dialogue discourse, which is a dialogue-specific structure that can provide pre-defined semantic relationships between each utterance. We first transform the entire meeting text with dialogue discourse relations into a discourse graph and then use DDA-GCN to encode the semantic representation of the graph. Finally, we employ a Recurrent Neural Network to generate the summary. In addition, we utilize the question-answer discourse relation to construct a pseudo-summarization corpus, which can be used to pre-train our model. Experimental results on the AMI dataset show that our model outperforms various baselines and can achieve state-of-the-art performance.