Focusing on subtractive color dyes currently used in dye-based color ink jet printers (IJs), we consider that it is important to increase the size of color gamut on high quality coated paper in particular. Development of the optimum subtractive color dyes will rely on full understanding of the relationship between dye amounts placed on the paper and resultant colors. In a previous study, the author verified that models were able to be used to predict the colorimetric gamut of a hypothetical dye set. Among the models, the Kubelka-Munk equation (KM) which relies only on the spectral reflectances of the primary colors achieved reproducible performance for the color gamut on coated paper used in a dye-based color IJ. Based on this result, the present study has used KM for prediction of the color gamut of a hypothetical dye set. The color gamut has been calculated by means of computer simulation, and the optimum combination of three dyes for a dye-based color IJ has been solved by constrained nonlinear programming. Moreover, the color gamut has been compared between the optimum three dyes obtained in this study and typical C, M and Y dyes for a dye-based color IJ. The result showed that the area of the color gamut obtained by the optimum combination of three dyes was only 1.1 times larger than that by the typical C, M and Y dyes, and the optimum peak wavelengths and absorption bandwidths depended on lightness.