We investigate the usage of edge-based inpainting as an intra prediction method in block-based image compression. The joint utilization of edge information and the well-known Laplace equation yields a simple and effective inpainting algorithm. As for intra prediction, the edge-based inpainting is a uniform solution, yet adaptive to local image features. During the integration of edge-based inpainting into a block-based coding scheme, edge extraction and coding are jointly considered to achieve the rate-distortion optimization. Our proposed schemes are compared with JPEG2000, and experimental results demonstrate that both PSNR gain and visible quality improvement are achieved.