A new type of color mapping method named ‘categorical color mapping’ is developed for gamut mapping. Categorical color mapping provides an optimal mapping point while maintaining a relative color-categorical relationship between a source space and a destination space. Existing techniques in the field of color science and engineering have been developed based on matching criteria. However, there has been no matching criterion for design of a gamut mapping algorithm due to difference in device gamut between a source space and a destination space. Therefore, gamut mapping has remained a critical issue in comparison with the existing techniques. In categorical color mapping, a new matching criterion named ‘categorical color matching’ is introduced for implementing a matching criterion into the design of gamut mapping. Because categorical color matching is based on a color naming experiment, categorical color mapping is intended to include the perceptual information of the human visual system. This is another factor that differentiates the proposed method from conventional techniques in addition to the implementation of the matching criterion. This article describes the theory of categorical color mapping and its effectiveness in comparison with conventional gamut mapping techniques.