In this paper, we present a fast image upsampling method within a two-scale framework to ensure the sharp construction of upsampled image for both large-scale edges and small-scale structures. In our approach, the low-frequency image is recovered via a novel sharpness preserving interpolation technique based on a well-constructed displacement field, which is estimated by a cross-resolution sharpness preserving model. Within this model, the distances of pixels on edges are preserved, which enables the recovery of sharp edges in the high-resolution result. Likewise, local high-frequency structures are reconstructed via a sharpness preserving reconstruction algorithm. Extensive experiments show that our method outperforms current state-of-the-art approaches, based on quantitative and qualitative evaluations, as well as perceptual evaluation by a user study. Moreover, our approach is very fast so as to be practical for real applications.