Color vector quantization is a very important technique to display a color image with N2, typically N equals 256, colors in a personal computer and workstation or print a color image with K, typically K equals 256, colors without too much color degradation. The LBG algorithm is a popular suboptimal algorithm to solve the color vector quantization. However, it is very slow. Several fast algorithms such as the popularity algorithm, the median cut algorithm have been proposed. In this paper, we propose a new fast algorithm for color vector quantization. The proposed algorithm has been implemented in a tree structure. Assume that n is the number of pixels in the image and m is the dimension of the color space. In the tree structure, there is n leaves in the tree in the worst case, where n is the total pixel numbers in the original color image. The storage complexity of the proposed algorithm is O(n) and the time complexity if O(n log2 N). It is much faster than the median cut algorithm. In the same space complexity O(mn) our algorithm has time complexity O(n log2 K) while the median cut algorithm requires O(m log2 Kn log2 n), where m equals 3 is the dimensionality of the color space. Also, our algorithm finds the centroid of a compact cube instead of a rectangular shape in the median cut algorithm. Therefore, it produces better color images after vector quantization.