In this paper, we present a new macroblock-based bit allocation scheme in multiple MPEG-1 video encoders system and a single multiplexer over a single channel. The proposed scheme models the relations between fate(Bits/MB) and distortion(MSE/MB), rate and quantizer parameter(QP), distortion and quantizer parameter, respectively, in the same form. By using these relations, we minimize the Larangian cost function to obtain a bit allocation scheme based on macroblock unit. Experimental results show that the proposed scheme can reduce MSE compared to other conventional buffer-based rate control methods, i.e. independent buffer control method and shared common buffer control one. And we confirmed, through computer simulation, that the proposed scheme can be effectively modified to maintain the objective quality of a specific video service at a constant level.