We propose a fast palette design scheme based on the K-means algorithm for color image quantization. To accelerate the K-means algorithm for palette design, the use of stable flags for palette entries is introduced. If the squared Euclidean distances incurred by the same palette entry in two successive rounds are quite similar, the palette entry is classified to be stable. The clustering process will not work on these stable palette entries to cut down the required computational cost. The experimental results reveal that the proposed algorithm consumes a lower computational cost than those comparative schemes while keeping approximately the same image quality.