In this paper, we propose an optimal bit rate control algorithm which is fully compatible with MPEG-4 or H.263+. The proposed algorithm is designed to identify the optimal quantizer set through Lagrangian optimization when used for optimal bit allocation. To find the optimal quantizer set, we make use of the Viterbi algorithm in order to solve the dependency between quantization parameters of each macroblock due to the unique characteristics of MPEG-4 or H.263+. We set the Lagrangian cost function as a cost function of the Viterbi algorithm. We implement the proposed algorithm in MPEG-4 coders and compare its performance to the VM8 and optimal bit rate control algorithm, using independent quantization parameters in the circumstance of a low bit rate.