In this paper, we propose a new method to allocate bandwidth adaptively according to the amount of input traffic volume for a long range dependent traffic requiring Quality of Service (QoS). In the proposed method, we divide the input process, which is modelled by an M/G/infinity input process, into two sub-processes, called a long time scale process and a short time scale process. For the long time scale process we estimate the required bandwidth using the linear prediction. Since the long time scale process varies (relatively) slowly, the required bandwidth doesn't need to be estimated frequently. On the other hand, for the short time scale process, we use the large deviation theory to estimate the effective bandwidth of the short time scale process based on the required QoS of the input traffic. By doing this we can capture the short time scale fluctuation by a buffer and the long time scale fluctuation by increasing or decreasing the bandwidth adaptively. Through simulations we verify that our proposed method performs well to satisfy the required QoS.