A new three dimensional fractal coding is proposed with a perceptually enhanced matching. Since most of medical images (e.g. computed tomoyaphy or magnetic resonance images) have three dimensional characters, searching regions are extended to adjacent slices. For a perceptually enhanced matching, a high frequency boost filter is used for pre-filtering images to be encoded, and a least mean square error matching is applied to the edge enhanced Images rather than the original images. From simulation with magnetic resonance images($255 imes255$, 8bits/pixel), reconstructed images by the proposed compression algorithm show much improved subjective image quality with higher peak signnal-to-noise ratio compared to those by existing fractal coding algorithms at compression ratios of about 10.