Differentiated Services (DiffServ)-aware network potentially can provide the next generation platform for multimedia support in the Internet. In this work we look at improving bandwidth allocation in such a network. We study how to implement bandwidth predicting and policing in a DiffServ aware network using fuzzy logic. A token bucket fuzzy logic bandwidth predictor for real time variable bit rate traffic class is proposed. Here, the AF traffic class is associated with real time variable bit rates traffic. The fuzzy logic bandwidth predictor facilitates bandwidth predicting and dynamic policing based on the class based packet aggregates. This improves the admission control of connections to the network. A simulation study was performed for the fuzzy logic predictor using Network Simulator-2. The simulation results show that the fuzzy logic predictor gave commendable bandwidth prediction value compared to a deterministic bandwidth allocation for the traffic class.