The Bianchi type-Ⅲcosmological model for a cloud string with bulk viscosity are studied. To obtain a determinate solution, it is assumed that the coefficient of bulk viscosity is a power function of the scalar of expansion ζ = kθm and the shear scalar is proportional to scalar of expansion σ∝θ, which leads to the relation between metric potentials B = Cn. The physical features of the model are also discussed. It is found that the power index mhas significant influence on the string model. There is a "big bang" start in the model when m ≤ 1 but there is no the big-bang start when m ＞ 1. In the special case m = 0, the model reduces to the string model of constant coefficient of bulk viscosity that was the result previously given in the literature.