We present a PaperRobot who performs as an automatic research writing assistant by (1) conducting deep and comprehensive understanding of a large collection of existing papers in an entire target domain and constructing a comprehensive background knowledge base (KB); (2) creating new ideas by predicting links from the background KB, based on a novel algorithm combining graph attention and contextual text attention; (3) incrementally writing some key elements of a new paper based on memory-attention networks: from the input title along with predicted related entities to generate a paper abstract, from the abstract to generate conclusion and future work, and finally from future work to generate a title for a follow-on paper. Turing Tests, where a biomedical domain expert is asked to compare the human-written published paper and the corresponding system-generated part for the same title, show that PaperRobot generated paper components are often chosen over human-written ones.