Recently, the theories and applications of complex networks have paid much attention in many fields of science and engineering.This paper investigates the stability of a symmetric network with long range connections by a probability p.The adjacent matrix A consists of a regular matrix Q and a random matrix R.By the spectral analysis and the matrix perturbation theory, we give an analysis about the effects of regular matrix A and random matrix R on the spectra of the adjacent matrix A, and then give a generalized sufficient condition to guarantees stability of this complex network.