A video encoding apparatus includes a plurality of encoders for encoding each of a plurality of video programs received from external; a multiplexer for multiplexing outputs of the plurality of encoding means; a buffer for temporarily storing and transmitting signal multiplexed by the multiplexer; and a central controller for receiving monitoring information with respect to buffer fullness from the buffer and providing quantization parameters to be applied to respective pictures to be now encoded with the respective encoders. The sum of the bit rates of all the multiplexed video programs is constant, but each of the video programs allows for a variable bit rate (VBR) by synchronously controlling each of a video encoders by means of the central controller, thereby maintaining a relatively uniform picture quality within one picture.