Images captured in weak illumination conditions will seriously degrade the image quality. Solving a series of degradation of low-light images can effectively improve the visual quality of the image and the performance of high-level visual tasks. In this paper, we propose a novel Real-low to Real-normal Network for low-light image enhancement, dubbed R2RNet, based on the Retinex theory, which includes three subnets: a Decom-Net, a Denoise-Net, and a Relight-Net. These three subnets are used for decomposing, denoising, and contrast enhancement, respectively. Unlike most previous methods trained on synthetic images, we collect the first Large-Scale Real-World paired low/normal-light images dataset (LSRW dataset) for training. Our method can properly improve the contrast and suppress noise simultaneously. Extensive experiments on publicly available datasets demonstrate that our method outperforms the existing state-of-the-art methods by a large margin both quantitatively and visually. And we also show that the performance of the highlevel visual task (i.e. face detection) can be effectively improved by using the enhanced results obtained by our method in lowlight conditions. Our codes and the LSRW dataset are available at: https://github.com/abcdef2000/R2RNet.