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In LEO satellites networks, dropping probability of handoff calls and blocking probability of new calls are two important QoS measures. In this paper, a new channel assignment strategy is proposed to improve QoS performance in low earth orbit satellite systems (LEO-MSSs). Different from previous channel assignment schemes, the proposed strategy is designed to improve the QoS performance of LEO-MSSs by decreasing the average times of handover along the calls duration instead of deducing failure probability of single handover request. In addition, recursive formulas are derived to deal with complexity of computing dropping probability of handoff calls and blocking probability of new calls. Numerical results reveal that the proposed scheme could effectively deduce the dropping probability and unsuccessful call probability.