This paper proposes a color image coding method based on recurrent iterated function systems (RIFSs). To encode a set of multispectral images, we apply a RiFS to multiset data consisting of three images. in the proposed method, the mappings not only between blocks within an individual spectral image but also between blocks of different spectral images are performed with contraction constraint. Simulation results show that the fractal coding based on the RiFS is useful for encoding concurrently a set of images by describing the similarity existing between a pair of images. In addition, the proposed color coding method can be applied to subband images and moving image sequences consisting of a set of images having similar gray patterns.