Single-image super-resolution (SR) is to reconstruct a high-resolution image from a low-resolution input image. Nevertheless, most SR algorithms are performed in an iterative manner and are therefore time-consuming. In this paper, we propose an iteration-free single-image SR algorithm based on fast deconvolution with gradient prior. Based on the prior calculated from the initially upsampled image via current approach (e.g., bicubic interpolation or example/learning-based approaches), we make the deconvolution process well-posed, which can be efficiently solved in FFT domain. Moreover, the proposed algorithm can be directly applied to video SR, where the temporal coherence can be automatically maintained. Experimental results demonstrate that the proposed method can simultaneously obtain significant acceleration and quality improvement over several existing SR methods.