In this study, the performance of ATM multiplexer with MPEG(Motion Pictures Experts Group) video is analyzed by considering the effect of the MPEG GOP(Group of Pictures) structure. By assuming that frame starting times are synchronized, aggregated traffics are considered to be transmitted at the beginning of each frame time units. The aggregated number of cells generated during a frame time unit is, therefore, derived from distributions of individual sources. The stationary probability of buffer occupancy can be easily obtained by using a property of the periodicity of aggregated traffics. Simulation approach is also used to determine the traffic load for a given probability of satisfying QoS(Quality of Service).