Document images captured in natural scenes with a hand-held camera often suffer from geometric distortions and cluttered backgrounds. In this paper, we propose a simple yet efficient deep model named Adversarial Gated Unwarping Network (AGUN) to rectify these images. In this model, the rectification task is recast as a dense grid prediction problem. We thereby develop a pyramid encoder-decoder architecture to predict the unwarping grid at multiple resolutions in a coarse-to-fine fashion. Based on the observation that the structural visual cues, e.g., text-lines, text blocks, lines in tables, which are critical for the estimation of unwarping mapping, are non-uniformly distributed in the images, three gated modules are introduced to guide the network focusing on these informative cues rather than other interferences such as blank areas and complex backgrounds. To generate more visually pleasing rectification results, we further adopt adversarial training mechanism to implicitly constrain the unwarping grid estimation. Our model can rectify arbitrarily distorted document images with complicated page layouts and cluttered backgrounds. Experiments on the public benchmark dataset and the synthetic dataset demonstrate that our approach outperforms the state-of-the-art methods in terms of OCR accuracy and several widely used quantitative evaluation metrics.