This paper proposes a channel reservation scheme for handovers which efficiently supports multi-class traffic in low earth orbit mobile satellite systems (LEO-MSS). Analytical methods are developed for evaluating the performance of priority-based multi-class traffic channel reservation scheme (PMCR). The new call blocking probability and handover failure probability of PMCR for each traffic are deduced. The simulation results verify the correctness and accuracy of the proposed scheme and show that the new call blocking probability of the system is lower than fixed channel reservation (FCR) and handover call performance of services of high levels can be improved by the introduction of priorities.