We focus on graph-to-sequence learning, which can be framed as transducing graph structures to sequences for text generation. To capture structural information associated with graphs, we investigate the problem of encoding graphs using graph convolutional networks (GCNs). Unlike various existing approaches where shallow architectures were used for capturing local structural information only, we introduce a dense connection strategy, proposing a novel Densely Connected Graph Convolutional Network (DCGCN). Such a deep architecture is able to integrate both local and non-local features to learn a better structural representation of a graph. Our model outperforms the state-of-the-art neural models significantly on AMR-to-text generation and syntax-based neural machine translation.