Through deriving the amplification formula of effective inter-storey displacement for triangle form steel outriggers, the formula of additional modal damping ratio for the high-rise building with damped rigid outriggers were presented. Taking the frame-core-tube structure as an example, the frame-core-tube structures with damped rigid outriggers, diagonal-brace damping layers, and strengthened storeys, respectively, under the action of pulse-like earthquake waves and non pulse-like earthquake waves were analyzed and compared. The computing results show that the structure with damped rigid outriggers exhibits the best seismic performance in the above three frame-core-tube structures, and the pulse-like earthquake waves make a great enhance on seismic performance of the high-rise buildings. Meanwhile, seismic performance of the structure with damped rigid outriggers is in proportion to the distance of shear wall to outside frame column, but inversely proportional to storey height, and related to the angle of viscous damper.