To improve the quality of the reconstructed image for a given bit rate constraint, the assigned bits must be distributed efficiently using a set of admissible quantizers so that source distortion can be minimized. The optimal bit allocation scheme for source coding is based on Shannon's rate-distortion theory, which deals with minimization of source distortion subject to a channel rate constraint. To allocate a given quota of bits to an arbitrary set of different quantizers, several fast algorithms have been suggested for optimal bit allocation. However, these methods are still not practical due to large computational burden. This paper proposes a new fast algorithm which needs less computing time than existing fast algorithms.