The sensitivity characteristics of the undamped natural frequencies and complex mode shapes of vibration system with the non-proportional viscous damping with respect to structural mass, stiffness and damping modifications are analyzed in this paper using the matrix perturbation of complex modes. The general principles for the selectivity of the design and the most sensitive positions of the structural perturbation modifications are shown thereby. This is of importance to a great computational savings in the dynamic characteristic improvement of large or complex structures. By the dynamic characteristic sensitivity analysis of a test device type RDT-1,the optimal structural design for its especial requirement of dynamic characteristics is obtained easily and the principles presented in this paper are confirmed by the numerical results of perturbation analysis.