Image completion involves filling missing parts in images. In this paper we address this problem through novel statistics of similar patches. We observe that if we match similar patches in the image and obtain their offsets (relative positions), the statistics of these offsets are sparsely distributed. We further observe that a few dominant offsets provide reliable information for completing the image. Such statistics can be incorporated into both matching-based and graph-based methods for image completion. Experiments show that our method yields better results in various challenging cases, and is faster than existing state-of-the-art methods.