Today's Internet can only support "best effort" traffic while with fast emerging multimedia services, it will become clear that the future Internet architecture will have to support various applications with different quality of service (QoS) requirements. The Differentiated Services (DiffServ) model allows the support of QoS Differentiated Services on an IP backbone network. The DiffServ model provides service classification by means of the Differentiated Service (DS) field in the IP header and the per hop behavior (PHB) observable behavior at the node. In this paper we propose a fuzzy based DiffServ model to implement the Differentiated Services in the Internet. In the proposed model we use a fuzzy meter which is based on a dynamic rate leaky bucket (LB) mechanism. Furthermore we use random early discard (RED) mechanism to provide low loss probability for Assured Services. Simulation results show that the proposed fuzzy DiffServ model has better performance than the conventional DiffServ model with leaky bucket meter.