A new fast algorithm that can display true 24-bits color images of JPEG and MPEG on a 8 bits color display is described. Instead of generating a colormap in the R-G-B color space conventionally, we perform analysis of color images based on the Y-Cr-Cb color space. By using Bayes decision rule, the representative values for Y component are selected based on its histogram. Then, the representative values for Cr and Cb components are determined by their conditional histogram assuming Y. Finally, a fast lookup table that can generate R-G-B outputs for Y-Cr-Cb inputs without matrix transformation is addressed. The experimental results show that good-looking quality color quantization images can be achieved by our proposed algorithm.