In general, subtractive color dyes used for current ink jet printers (IJs) are selected from among many potential dyes. However, such trial-and-error approaches are inefficient, and there remain questions as to how to guarantee a truly optimum dye set. Thus, development of a computer simulation system to choose the optimum subtractive color dyes is an important goal. Recently, IJs have been rapidly advancing. Among a variety of factors controlling image quality of dye-based color IJs, color gamut has been improved considerably by increasing the number of inks.In the previous study, the models were studied from the viewpoint of prediction accuracy for colorimetric color reproduction. Among the models, KM that relies only on the reflectances of the primary colors approximately reproduced the color gamut. Based on the result above, this study has been solved the optimum color dyes for spectral and colorimetric color reproduction by means of a computer simulation. The former is to obtain the optimum dye set for minimizing RMS spectral reflectance error between measured and reproduced spectral reflectances for Macbeth Color Checker that is composed of 24 printed color squares, and the latter is to obtain the optimum dye set for maximizing the size of color gamut between L*=40 and L*=80 under D65 and 2° observer.