Color quantization is used to obtain an image with the same number of pixels as the original but represented using fewer colors. Most existing color quantization algorithms are based on the Red Green Blue (RGB) color space, and there are few color quantization algorithms for the Hue Saturation Intensity (HSI) color space with a simple uniform quantization algorithm. In this paper, we propose a dichotomy color quantization algorithm for the HSI color space. The proposed color quantization algorithm can display images with a smaller number of colors than other quantization methods of RGB color space. The proposed algorithm has three main steps as follows: first, a single-valued monotonic function of the Hue (H) component in the from RGB color space to HSI color space (RGB-HSI) color space conversion is constructed, which can avoid the partition calculation of the H component in the RGB-HSI color space; second, an iterative quantization algorithm based on the single-valued monotonic function is proposed; and third, a dichotomy quantization algorithm is proposed to improve the iterative quantization algorithm. Both visual and numerical evaluations reveal that the proposed method presents promising quantization results.