This paper suggests techniques to enhance coding time which is a problem in traditional fractal compression and to improve fidelity of reconstructed images by determining fractal coefficient through adaptive selection of block approximation formula. First, to reduce coding time, we construct a linear list of domain blocks of which characteristics is given by their luminance and variance and then we control block searching time according to the first permissible threshold value. Next, when employing three-level block partition, if a range block of minimum partition level cannot find a domain block which has a satisfying approximation error, There applied to 24-bpp color image compression and image techniques. The result did not occur a loss in the image quality of the image when using the encoding method, such as almost to the color in the RGB image compression rate and image quality, such as gray-level images and showed good.