Abstract: This paper studies the growing networks with linear preferential attachment The recursive formula of degree distribution is presented. we prove that the approximate analytical solution of the recursive formula is in accordance with Mandelbrot law distribution p（k）∝（k+c）γ in certain conditions and then we obtain the concrete expressions of the scaling exponent γ and the shifting coefficient c. It is concluded that there is a deviation of shifting coefficient c in the approximation of traditional difference analysis. The accuracy of this method is confirmed by numerical experiments.