In this paper, we propose least-squares images (LS-images) as a basis for a novel edge-preserving image smoothing method. The LS-image requires the value of each pixel to be a convex linear combination of its neighbors, i.e., to have zero Laplacian, and to approximate the original image in a least-squares sense. The edge-preserving property inherits from the edge-aware weights for constructing the linear combination. Experimental results demonstrate that the proposed method achieves high quality results compared to previous state-of-the-art works. We also show diverse applications of LS-images, such as detail manipulation, edge enhancement, and clip-art JPEG artifact removal.