Fractal　image　compression　is　a　relatively　recent　image　compression　method.　Its　extension　to　a　sequence　of　motion　images　is　important　In　video　compression　applications.　There　are　two　basic　fractal　compression　methods,　namely　the　cube-based　and　the　frame-based　methods,　being　commonly　used　in　researches.　This　paper　proposes　a　cuboid　algorithm.　In　this　algorithm　the　steps　of　three　directions　may　be　changed　respectively　so　the　compression　ratio　can　be　varied　according　to　the　quality　of　decompressed　image　sequences.　The　experimental　results　show　that　a　high　quality　of　decompressed　image　sequences　can　be　obtained　with　a　relative　high　compression　ratio.