This paper presents a novel neural machine translation model which jointly learns translation and source-side latent graph representations of sentences. Unlike existing pipelined approaches using syntactic parsers, our end-to-end model learns a latent graph parser as part of the encoder of an attention-based neural machine translation model, and thus the parser is optimized according to the translation objective. In experiments, we first show that our model compares favorably with state-of-the-art sequential and pipelined syntax-based NMT models. We also show that the performance of our model can be further improved by pre-training it with a small amount of treebank annotations. Our final ensemble model significantly outperforms the previous best models on the standard English-to-Japanese translation dataset.