SummaryThe application of the outrigger technology effectively improves the lateral stiffness of buildings, reduces harmful deformation, enhances the seismic resistance of structures, and contributes to the rapid development of high‐rise buildings. To improve the response speed and energy dissipation of a viscous damping outrigger under seismic excitation, a viscous damping outrigger with an amplifier was proposed, and its effectiveness was verified by combining it with the seismic design of a 149.2 m high‐rise building in an 8.5‐degree intensity area. To determine the additional damping ratio of the building structure, investigations were carried out using both the code method and energy ratio method to evaluate the contribution of the damping outrigger. The damped outrigger equivalent stiffness determination method was studied, and the simplified engineering calculation method was compared against the refined finite element analysis results for engineering design purposes. The displacement amplification technique incorporated into the viscously damped outrigger can enhance the damper response speed, and increase the energy dissipation of the damped outrigger system. The application of an enlarged damped outrigger in engineering can result in an additional damping ratio of approximately 1% while simplifying the calculation method based on the additional damping and equivalent damper cut‐line stiffness, which can be useful in engineering design.