The mobile cellular systems are expected to support multiple services with guaranteed Quality of Service (QoS). However, the ability of wireless systems to accommodate expected growth of traffic load and broadband services is limited by available radio frequency spectrum. Call Admission Control (CAC) is one of the resource management functions, which regulates network access to ensure QoS provisioning. However, the decision for CAC is very challenging issue due to user mobility, limited radio spectrum, and multimedia traffic characteristics. To deal with these problems, in this paper, we propose a fuzzy CAC system. We compare the performance of the proposed system with Shadow Cluster Concept (SCC). We evaluate by simulation the performance of the proposed system. The proposed system has a good behavior on deciding the number of accepted connections while keeping the QoS for serving connections.