A novel approach is proposed that leads to the design and evolution of a scale-free network that satisfies any given power-law distribution.The approach makes use of another important feature of the scale-free network: the final formation of a scale-free network is controlled by the geometric mean of its degrees.Therefore,an algorithm is provided: starting from a rational small-world network,continuously deleting or adding an edge from or to the network by the "rich get richer" principle,meanwhile keeping the total number of nodes,the total number of edges and the connectivity of the network unchanged,until the geometric mean of the degrees of the network reaches a certain value,a prerequisite scale-free network will be formed.Numerical simulations show that the above algorithm can always lead to the evolution of a scale-free network that satisfies any given power-law distribution.