An important issue of resource distribution is the fairness of the distribution. For example, computer network management wishes to distribute network resource fairly to its users. To describe the fairness of the resource distribution, a quantitative fairness score function F (x1, x2., xn) was proposed in 1984 by Jain et al. The purpose of this paper is to propose a modified network sharing fairness function so that the users can be treated differently according to their priority levels. The mathematical properties are discussed. The proposed fairness score function F < (x1, x2., xn; w1, w2., wn) keeps all the nice properties of F (x1, x2., xn) and provides better performance when the network users have different priority levels.