A structural system composed of a moment frame and a shear wall connected with viscous damper is investigated through time history analysis for ground motion. The new system is compared with an usual dual system, in which moment frames and shear walls are connected rigidly, and a system utilizing both connecting methods complexly. Applicability of the modal strain energy method to initial estimation of required damping coefficients is verified. Finally, reduction of the wall length by installing viscous damper connections is investigated. The new system mitigates the roof displacement and maximum inter-story drift of the moment frame more effectively than the conventional rigid connection system with smaller requirement on the wall stiffness.