Abstract: Document-level machine translation (MT) remains challenging due to its difficulty in efficiently using document-level global context for translation. In this paper, we propose a hierarchical model to learn the global context for document-level neural machine translation (NMT). This is done through a sentence encoder to capture intra-sentence dependencies and a document encoder to model document-level inter-sentence consistency and coherence. With this hierarchical architecture, we feedback the extracted document-level global context to each word in a top-down fashion to distinguish different translations of a word according to its specific surrounding context. Notably, we explore the effect of three popular attention functions during the information backward-distribution phase to take a deep look into the global context information distribution of our model. In addition, since large-scale in-domain document-level parallel corpora are usually unavailable, we use a two-step training strategy to take advantage of a large-scale corpus with out-of-domain parallel sentence pairs and a small-scale corpus with in-domain parallel document pairs to achieve the domain adaptability. Experimental results of our model on Chinese-English and English-German corpora significantly improve the Transformer baseline by 4.5 BLEU points on average which demonstrates the effectiveness of our proposed hierarchical model in document-level NMT.