Abstract: An approximateapproach based on the direct modal perturbation method is suggested foranalyzing the complex modal characteristics of non-proportional dampingstructure systems. The proposed approach uses the expansion of complex Ritz vectors. The procedure is in two steps. First, thesubspace of the solution based on the complex vectors is formed by using theconventional real modes of the structure. Then, a set of solutions ofnon-linear complex algebraic equations is established to displace thesolution of the complex eigen-value equations. The results of two numericalexamples show that the suggested method simplifies the solving procedure andis of high precision and efficiency. It can be used for the solution of thecomplex modal characteristics and dynamic responses of non-proportionaldamping structure systems.