The present invention introduces an apparatus and method for securing a constant bit rate in transmitting various types of media data through multiplexing over an ATM network so as to achieve a constant bit rate communication. Received video/audio information from an information source is encoded at an information source encoder and outputted to a media multiplexer as encoded video/audio information. The media multiplexer multiplexes encoded the video/audio information to obtain fixed-length data as transmission data. The media multiplexer, upon reception of a transmission enable signal from a line interface unit, transmits the transmission data to the line interface unit. The line interface unit assembles the transmission data on an ATM cell format basis and transmits cell data,over the ATM network.