Compared to tree grammars, graph grammars have stronger generative capacity over structures. Based on an edge replacement grammar, in this paper we propose to use a synchronous graph-to-string grammar for statistical machine translation. The graph we use is directly converted from a dependency tree by labelling edges. We build our translation model in the log-linear framework with standard features. Large-scale experiments on Chinese–English and German–English tasks show that our model is significantly better than the state-of-the-art hierarchical phrase-based (HPB) model and a recently improved dependency tree-to-string model on BLEU, METEOR and TER scores. Experiments also suggest that our model has better capability to perform long-distance reordering and is more suitable for translating long sentences.