The fuzzy C-means (FCM) algorithm has two major problems for the codebook design: tremendous memory requirement and intensive computation. This paper presents two codebook design algorithms based on FCM. The first algorithm overcomes the storage problem with the use of the codebook, rather than the membership matrix in FCM, to initiate and terminate the algorithm. A fast version is presented to further solve the computation problem. The fast algorithm partitions a training set into several classes and then the first algorithm is applied to each class separately. Experimental results show that both new algorithms achieve better picture quality. Furthermore, the fast algorithm is obviously faster than LBG and FCM.