Most existing superresolution (SR) techniques focus primarily on improving the quality in the luminance component of SR images, while paying less attention to the chrominance component. We present an edge and color preserving image SR approach. First, for the luminance channel, a heavy-tailed gradient distribution of natural images is investigated as an image prior. Then, an efficient optimization algorithm is developed to recover the latent high-resolution (HR) luminance component. Second, for the chrominance channels, we propose a two-stage framework for luminance-guided chrominance SR. In the first stage, since most of the shape and structural information is contained in the luminance channel, a simple Markov random field formulation is introduced to search the optimal direction for color local interpolation guided by HR luminance components. To further improve the quality of the chrominance channels, in the second stage, a nonlocal auto regression model is utilized to refine the initial HR chrominance. Finally, we combine the SR reconstructed luminance components with the generated HR chrominance maps to get the final SR color image. Systematic experimental results demonstrated that our method outperforms some state-of-the-art methods in terms of the peak signal-to-noise ratio, structural similarity, feature similarity, and the mean color errors.