Recent studies on AMR-to-text generation often formalize the task as a sequence-to-sequence (seq2seq) learning problem by converting an Abstract Meaning Representation (AMR) graph into a word sequences. Graph structures are further modeled into the seq2seq framework in order to utilize the structural information in the AMR graphs. However, previous approaches only consider the relations between directly connected concepts while ignoring the rich structure in AMR graphs. In this paper we eliminate such a strong limitation and propose a novel structure-aware self-attention approach to better model the relations between indirectly connected concepts in the state-of-the-art seq2seq model, i.e. the Transformer. In particular, a few different methods are explored to learn structural representations between two concepts. Experimental results on English AMR benchmark datasets show that our approach significantly outperforms the state-of-the-art with 29.66 and 31.82 BLEU scores on LDC2015E86 and LDC2017T10, respectively. To the best of our knowledge, these are the best results achieved so far by supervised models on the benchmarks.