VBR compressed, pre-recorded video is known to exhibit significant, multiple time-scale bit rate variability. To reduce the variability and burstiness of the aggregated transmission rate as low as possible, in this paper, we present an adaptive bandwidth smoothing algorithm, that can be effectively applicalble for VoD services over a shared-medium channel. For these environments where many clients are connected to a single server, by introducing the conventional MVBA(minimum variability bandwidth allocation) algorithm and controlling adaptively the conventional MVBA(minimum variability bandwidth asllocation) algorithm and controlling adaptively the aggregated transmission rate whenever a new clients request is arrived at the server side, the proposed algorithm effectively reduces the burstiness and variability of the aggregated transmission rate. Through computer experiments, it is shown that the proposed method perporms better than the convertional non-aggregated bandwidth smoothing schemes in terms of the peak rate, standard deviation, number of rate changes for the aggregated traffic.