Abstract: Energy dissipation mechanism, such as viscous damping, is dramatically beneficial to improve seismic resilience of earthquake resilient dual-systems. At the same time, large amounts of viscous damping make this system have more significant non-proportional damping characteristics, which leads to a large error when calculating response by using the traditional mode superposition method. Aiming at establishing a seismic resilience-oriented design method for this system with previous research, the complex mode orthogonality conditions are derived first for the distributed parameter model of the system, and then the complex mode superposition method is developed for computing its dynamic response under base excitations. Two applications are conducted with this method after verification: response calculation error analysis of the traditional mode superposition method, and choice of design parameters. It is found that: compared with the mode superposition method which only has fairly good calculation accuracy provided that the non-proportional damping is not significant, the complex mode superposition method performs better on calculation accuracy and on quantifying the control effect of viscous damping, which is helpful to design this system.