Abstract: The paper presents an approximate method for reanalysis of topological modification of non-classical damping structure with added degrees of freedom (DOF). The method，which is based on reduced model of original and topological structures, is followed by introducing dynamic condensation and singular value decomposition of complex matrix, and then combining the Rayleigh quotient inverse iteration method to obtain the final results. The results of numerical examples show that the suggested method can provide good approximation solutions with high precision, and it is very effective and feasible.