<p>This paper presents an optimal design methodology and a comprehensive seismic performance assessment for an outrigger system augmented with a tuned viscous mass damper (TVMD). In the proposed TVMD-outrigger configuration, the TVMD is installed between the outrigger and the perimeter columns, where it dissipates seismic energy through the amplified relative motion between the core tube and the perimeter columns. To facilitate the design procedure, the core tube’s behavior is decoupled into a modal single-degree-of-freedom (SDOF) system using a pseudo-mode superposition approach for the cantilever beam. The optimal frequency and damping ratios of the TVMD are determined by combining the fixed-point method with minimization of the <i>H</i>_∞- and <i>H</i>₂-norms of the displacement and acceleration amplification factors. A parametric analysis was conducted to verify the accuracy of the developed optimal methodology and to investigate the influences of the mass ratio and outrigger location on the design parameters. The frequency response function and time history analyses were subsequently performed to identify the control characteristics of the TVMDs designed using the displacement criterion for the first mode (TVMD₁) and the acceleration criterion for the second mode (TVMD₂). Numerical simulation results demonstrate that the TVMD₁ significantly suppresses the displacement demand, whereas the TVMD₂ is more efficient in mitigating the floor acceleration, the harmful inter-story drift ratio and shear force. Both TVMD configurations also achieve a superior reduction in overall input earthquake energy and demand on the structural elements. The proposed TVMD-outrigger systems reduced the maximum top-floor displacement and acceleration by up to 34.9% and 54.5%, respectively. Furthermore, practical engineering applications demonstrate the effectiveness of TVMD in providing supplemental damping and enhancing control efficiency in high-rise buildings.</p>