We propose a stable feedback control algorithm of the buffer state using the controlled Lagrange multiplier in combined rate-distortion characteristics for a buffer-constrained adaptive quantization. The proposed algorithm is established using feedback control theory and is described by the state equation with nonlinearity in the feedback path. The nonlinearity of the state equation comes from the average distortion-rate curve of the information source. The stability of this buffer control algorithm is shown using Lyapunov stability theory. It is shown that the stability of the algorithm depends on average distortion-rate curve and buffer size, and sufficient conditions for the algorithm to be stable are obtained from the usual average distortion-rate curve. In addition, it is observed from experimental results that the performance of the proposed algorithm and the optimal algorithm is not significantly different. Although the proposed algorithm does not provide optimal performance, the algorithm can be implemented easily with quite low computational complexity, as compared with others.< >