This paper addresses single image super-resolution (SR) based on convolutional neural networks (CNNs). It is known that recovery of high-frequency components in output SR images of CNNs learned by the least square errors or least absolute errors is insufficient. To generate realistic high-frequency components, SR methods using generative adversarial networks (GANs), composed of one generator and one discriminator, are developed. However, when the generator tries to induce the discriminator's misjudgment, not only realistic high-frequency components but also some artifacts are generated, and objective indices such as PSNR decrease. To reduce the artifacts in the GAN-based SR methods, we consider the set of all SR images whose square errors between downscaling results and the input image are within a certain range, and propose to apply the metric projection onto this consistent set in the output layers of the generators. The proposed technique guarantees the consistency between output SR images and input images, and the generators with the proposed projection can generate high-frequency components with few artifacts while keeping low-frequency ones as appropriate for the known noise level. Numerical experiments show that the proposed technique reduces artifacts included in the original SR images of a GAN-based SR method while generating realistic high-frequency components with better PSNR values in both noise-free and noisy situations. Since the proposed technique can be integrated into various generators if the downscaling process is known, we can give the consistency to existing methods with the input images without degrading other SR performance.