In this paper, we present a method of improving the quality of service in mobile cellular systems based on prioritization of handover requests. The objective here is to improve perceived quality of cellular service by minimizing both the probability of forced termination of ongoing calls due to handover failures and the degradation in spectrum utilization. We develop a model based on a nonpreemptive priority queueing discipline. New calls, which originate within the cell at a Poisson rate, are blocked if all channels are occupied. Handover requests are queued such that as soon as a channel is available, it is offered to the mobile subscriber with the measurement results closest to the minimum acceptable power level for communication. Handover requests arrive with a Poisson distribution and are queued if no channel is available at the time of arrival. The queue is dynamically reordered as new measurement results are submitted. Service rate is given by channel occupancy time distribution and is assumed to be exponential. The performance criteria of interest are: probability of handover failure, probability of call blocking, delay, and carried versus offered traffic. The performance of a cellular system employing the proposed handover policy is evaluated by simulation and compared. Furthermore, the results are compared to those obtained when the cellular system employs nonprioritized call handling and first-in/first-out (FIFO) queueing discipline. The new scheme is seen to provide lower probability of forced termination, less call blocking, less reduction in traffic, and less delay than the single-priority class FIFO queueing under all traffic conditions.