The influence of saturation property of cold nuclear matter on the parameterization process of fusion barriers are systematically studied using the double-folding procedure supplemented with the effect of Pauli repulsive interaction between two colliding nuclei. We obtain simple analytical expressions for calculating the fusion barrier position RB, height VB and curvature h¯ωB with and without the repulsion effects to evaluate the heavy-ion fusion cross sections. We have studied 90 heavy-ion fusion reactions with 64 ≤ Z1Z2 ≤ 1520 for charge product of the projectile and the target nuclei. The obtained results reveal that our parameterized formulae can reproduce the exact and experimental values of the fusion barrier characteristics with acceptable accuracy for the selected mass range. We calculate the theoretical values of the fusion cross sections using the parameterized values of RB, VB and h¯ωB. The comparison between the calculated and measured values of the fusion cross section at energies near and above the Coulomb barrier validates the quality of the presently obtained formulae. A discussion is also presented about the validity of the previous pocket formulae for fusion barriers in our selected mass range

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