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Scarcity of the spectrum resource and mobility of users make quality-of-service (QoS) provision a critical issue in cellular mobile multimedia networks. This paper presents a fuzzy call admission control scheme to meet the requirement of the QoS while prioritizing handoff call requests over new call requests. It searches automatically the number of the guard channel in a base station to make an effective use of resource and guarantee the QoS provision. A performance measure is formed as a weighted linear function of new call and handoff call blocking probabilities of each service class. Simulation compares the proposed fuzzy scheme with some well-known policies. Simulation results show that fuzzy scheme has a better robust performance in terms of average blocking criterion.