In most studies on learning-based image super-resolution (SR), the paired training dataset is created by downscaling high-resolution (HR) images with a predetermined operation (e.g., bicubic). However, these methods fail to super-resolve real-world low-resolution (LR) images, for which the degradation process is much more complicated and unknown. In this paper, we propose an unpaired SR method using a generative adversarial network that does not require a paired/aligned training dataset. Our network consists of an unpaired kernel/noise correction network and a pseudo-paired SR network. The correction network removes noise and adjusts the kernel of the inputted LR image; then, the corrected clean LR image is upscaled by the SR network. In the training phase, the correction network also produces a pseudo-clean LR image from the inputted HR image, and then a mapping from the pseudo-clean LR image to the inputted HR image is learned by the SR network in a paired manner. Because our SR network is independent of the correction network, well-studied existing network architectures and pixel-wise loss functions can be integrated with the proposed framework. Experiments on diverse datasets show that the proposed method is superior to existing solutions to the unpaired SR problem.