Following the recently proposed total variation (TV) up-sampling method, we present a novel image up-sampling algorithm based on fractional-order bidirectional diffusion. For the bidirectional diffusion, the forward diffusion occurs on the light side of edge, while the backward diffusion proceeds on the dark side. This bidirectional diffusion can reduce the edge width and avoid the appearances of false edge or texture and block effects. Moreover, the fractional-order derivative is used to avoid strong contrast near the edge in the interpolated images. The experiments show that, unlike the TV up-sampling (TVUP) method, the proposed algorithm does not suffer from the drift of edges, block effect in the smooth regions, false edges, and false texture.