The use of Hilbert scan is relatively new in image compression. This scan is guided by the Hilbert space-filling curve. A Hilbert image, thus produced by this scan of a graylevel image provides better compression rate than that of a raster scanned image. Since a Hilbert image is a 1-d image, an efficient 1-d algorithm based on Bezier-Berntein polynomial has been developed to simultaneously separate out and approximate homogeneous segments of pixels depending on some absolute error based criteria. Huffman coding scheme then encodes the approximation parameters. Investigation shows that better performance on image compression can be achieved using Hilbert scan. Comparison with an existing algorithm shows also better performance of the proposed algorithm.