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This paper investigates an analytical model of a channel allocation algorithm with a finite population of users in mobile cellular networks. The recursive formulas are derived for the new call blocking and handoff dropping probabilities of the Finite Population Fractional Guard Channel policies. The Fractional Guard Channel policy reserves a non-integral number of guard channels for handoff calls by rejecting new calls that depend on the current channel occupancy. The effect of users? mobility on the maximum system capacity is achieved when the Finite Population Uniform Fractional Guard Channel (FPUFGC) policy is evaluated. It is shown that FPUFGC policy performs better than Finite Population Guard Channel policy under the low handoff/new traffic ratio. An optimal parameter of FPUFGC minimises the blocking probability subject to the constraint on the dropping probability. Numerical results show that the proposed policy gives an improved system performance, compared to the most commonly used handover algorithms.