Abstract Document Grounded Conversations is a task to generate dialogue responses when chatting about the content of a given document. Obviously, document knowledge plays a critical role in Document Grounded Conversations, while existing dialogue models do not exploit this kind of knowledge effectively enough. In this paper, we propose a novel Transformerbased architecture for multi-turn document grounded conversations. In particular, we devise an Incremental Transformer to encode multi-turn utterances along with knowledge in related documents. Motivated by the human cognitive process, we design a two-pass decoder (Deliberation Decoder) to improve context coherence and knowledge correctness. Our empirical study on a real-world Document Grounded Dataset proves that responses generated by our model significantly outperform competitive baselines on both context coherence and knowledge relevance