Abstractive summarization is the ultimate goal of document summarization research, but previously it is less investigated due to the immaturity of text generation techniques. Recently impressive progress has been made to abstractive sentence summarization using neural models. Unfortunately, attempts on abstractive document summarization are still in a primitive stage, and the evaluation results are worse than extractive methods on benchmark datasets. In this paper, we review the difficulties of neural abstractive document summarization, and propose a novel graph-based attention mechanism in the sequence-to-sequence framework. The intuition is to address the saliency factor of summarization, which has been overlooked by prior works. Experimental results demonstrate our model is able to achieve considerable improvement over previous neural abstractive models. The data-driven neural abstractive method is also competitive with state-of-the-art extractive methods.