Traditional image compression algorithms are mostly based on L norm. However

those methods are not able to precisely control the error of each point. In this paper a maximum error image shift compression algorithm based on L norm is proposed. The algorithm can guarantee that the error at each point of the reconstructed image is limited in a given range. First，the algorithm takes the advantage of the image pixel similarity to decompose the image into many non-overlapping sub-blocks. Then each sub-block should be completely shifted

and the retained shift coefficients must be stored. Finally

the original image can be reconstructed by the retained shift coefficients. The experimental results show that

the suitable block size of the images of different resolutions is not the same

which increases by the increase of image resolution. Compared with the existing algorithm based on L norm maximum error shift compression

the compression ratio

reconstructed image quality and compression speed can be improved by the proposed algorithm.