In color image processing, hue-preserving is necessary for human being. In order to preserve the hue component, the perceptual color spaces such as HSI and HSV were used for the color image processing. The Hue-Saturation-Intensity (HSI) color space is important for color image processing and many color applications are commonly based on this color space. However, the gamut of conventional HSI color space is larger than that of RGB color space. Thus, the gamut problem is often occurred after the processing intensity and saturation in the HSI color space. In this paper, a new HSI color space with completely same gamut of RGB color space is developed. The gamut problem is solved by the proposed HSI color space.