Abstract meaning representation (AMR)-to-text generation is the challenging task of generating natural language texts from AMR graphs, where nodes represent concepts and edges denote relations. The current state-of-the-art methods use graph-to-sequence models; however, they still cannot significantly outperform the previous sequence-to-sequence models or statistical approaches. In this paper, we propose a novel graph-to-sequence model (Graph Transformer) to address this task. The model directly encodes the AMR graphs and learns the node representations. A pairwise interaction function is used for computing the semantic relations between the concepts. Moreover, attention mechanisms are used for aggregating the information from the incoming and outgoing neighbors, which help the model to capture the semantic information effectively. Our model outperforms the state-of-the-art neural approach by 1.5 BLEU points on LDC2015E86 and 4.8 BLEU points on LDC2017T10 and achieves new state-of-the-art performances.