Recent works in cyber deception study how to deter malicious intrusion by generating multiple fake versions of a critical document to impose costs on adversaries who need to identify the correct information. However, existing approaches are context-agnostic, resulting in sub-optimal and unvaried outputs. We propose a novel context-aware model, Fake Document Infilling (FDI), by converting the problem to a controllable mask-then-infill procedure. FDI masks important concepts of varied lengths in the document, then infills a realistic but fake alternative considering both the previous and future contexts. We conduct comprehensive evaluations on technical documents and news stories. Results show that FDI outperforms the baselines in generating highly believable fakes with moderate modification to protect critical information and deceive adversaries.