Abstract: This study presents the seismic mitigation investigation subjected to white-noise excitation for Dual Damping Tuned Mass Damper (DD-TMD) that combines viscous damping with hysteretic damping. To begin with, the configuration, advantages, and applications of DD-TMD are introduced, and the mechanism for DD-TMD is summarized. H₂ optimization for DD-TMD is proposed to obtain the optimal parameters through the algebraic solution, and the design process for DD-TMD is carried out. In addition, the effective additional viscous damping of the DD-TMD is further illustrated upon the H₂ optimization for DD-TMD, which lay an application foundation for pertinent engineering design. As a real application of DD-TMD, Variable Friction Pendulum Tuned Mass Damper (VFP-TMD) was applied as an illustration of DD-TMD to verify the effectiveness of the proposed methods for vibration control subjected to 20 sets of earthquake records. Results indicated that DD-TMD with H₂ optimization provided a comparative advantage on seismic mitigation capacity toward conventional viscous damping TMD. The equivalent viscous damping had successfully performed the constant friction damping by stochastic linearization method, indicating that H₂ optimization based on DD-TMD provided a reliable and functional design process for the VFP-TMD with inevitable initial friction coefficient. Compared with the former study on VFP-TMD by numerical searching method, the proposed DD-TMD design process with H₂ optimization performes better on seismic control performance and improved 16.6% of damping energy dissipation capacity.