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Recently, digital image inpainting technique based on variational and partial differential equation has been researched widely. In this paper, image inpainting is applied to image encoding and a novel scheme of encoding is proposed. In the encoding, applying an edge detector to detect the edge. In addition, the four boundaries of the image also belong to the edge collection; next, generating small neighborhoods of the edge collection to get an edge-extended image, then encoding the addresses of the edge-extended image and using high bit rate to accurately code the gray values of it. So, a high compression rate is achieved. Unlike the traditional decoding, here the decoding is realized by a harmonic inpainting model to achieve a good quality of reconstructed image. At the end, a lot of images are simulated. These simulated results show that with this scheme proposed, one can get a good quality of reconstructed image in a high compression rate. Keywords-image encodingt;image decoding; image inpaintingI.