In this paper, we consider color gamut multi-dimensionally for optimal constellation design in the color-space-based modulation methods. If points of some symbols are outside the three-dimensional color gamut, this can be a serious problem such as non-uniformity of the target color and the degradation of SER performance. Therefore, we propose the constraints in three-dimensional color gamut essential in the constellation design. Finally, through simulation, we demonstrate that the accurate and valid SER performance is obtained by considering the color gamut constraints. Finally, through simulation, we analyze the SER performance of color-space-based modulation under the color gamut constraints.