We present a novel method for single-image super-resolution (SR). In natural images, spatial edges usually have smooth contours. From this observation, we derive a fast edge-preserving natural image prior using our proposed fast edge-directed interpolation (EDI) method, and combine this prior with the wellknown sparse gradient prior into a maximum-a-posteriori (MAP) formulation of the SR problem. We develop an efficient primaldual algorithm to solve the inverse problem. The application of our edge-preserving prior adds little computational overhead and the output produced by our method demonstrates that results are better than those of the state-of-the-art conventional methods.