The novel passive energy dissipation system named Damped Outrigger System for frame-core tube structure is introduced in recent years, in which the outrigger and perimeter columns are separate, and the vertically acting fluid-viscous dampers connect the end of each of the outrigger walls to the adjacent perimeter column. In this paper, a new simplified model of this structure is studied by considering the damping force and shear stiffness of the core tube and lateral stiffness of the frame with finite element method. The shear correction factor is also employed to consider the shape of the core tube cross section. The numerical example shows that the displacement and the inter-story drift of the structure are reduced effectively under earthquake loads. It means that the damped outrigger is an innovative solution to resisting earthquake loads for frame-core tube structure.