Low-dose computed tomography (LDCT) has drawn major attention in the medical imaging field due to the potential health risks of CT-associated X-ray radiation to patients. Reducing the radiation dose, however, decreases the quality of the reconstructed images, which consequently compromises the diagnostic performance. Over the past few years, various deep learning techniques, especially generative adversarial networks (GANs), have been introduced to improve the image quality of LDCT images through denoising, achieving impressive results over traditional approaches. GAN-based denoising methods usually leverage an additional classification network, i.e., discriminator, to learn the most discriminate difference between the denoised and normal-dose images and, hence, regularize the denoising model accordingly; it often focuses either on the global structure or local details. To better regularize the LDCT denoising model, this article proposes a novel method, termed DU-GAN, which leverages U-Net-based discriminators in the GAN framework to learn both global and local differences between the denoised and normal-dose images in both image and gradient domains. The merit of such a U-Net-based discriminator is that it can not only provide the per-pixel feedback to the denoising network through the outputs of the U-Net but also focus on the global structure in a semantic level through the middle layer of the U-Net. In addition to the adversarial training in the image domain, we also apply another U-Net-based discriminator in the image gradient domain to alleviate the artifacts caused by photon starvation and enhance the edge of the denoised CT images. Furthermore, the CutMix technique enables the per-pixel outputs of the U-Net-based discriminator to provide radiologists with a confidence map to visualize the uncertainty of the denoised results, facilitating the LDCT-based screening and diagnosis. Extensive experiments on the simulated and real-world datasets demonstrate superior performance over recently published methods both qualitatively and quantitatively. Our source code is made available at https://github.com/Hzzone/DU-GAN .