Abstract: Recently, the novel TMDs that damping force linear with relative displacement were carried out. However, the parameters optimization process of it were mostly belonged to the field of dynamic numerical analysis, where the optimal parameter solutions are lacked. Presents the mitigation study for Hysteretic Damping Tuned Mass Damper (HD-TMD) which exhibits the property subjected to white-noise excitation. Starting with summarizing the mechanism for the HD-TMD, the relative equations of motion for structure-HD-TMD system are derived. H₂ optimization and performance balance optimization for HD-TMD are proposed to obtain the optimal parameters of numerical solutions through curve fitting and the performance balance procedure based on tolerate ratio. As a real application of HD-TMD, Variable Friction Pendulum Tuned Mass Damper (VFP-TMD) was applied as an illustration of HD-TMD to verify the effectiveness of the proposed methods for vibration control subjected to wind excitations. Results indicated that both H₂ optimization and performance balance design provided a better performance for HD-TMD rather than the traditional viscous damping TMD. Although the optimal parameters optimized by H₂ optimization can maximize the potential of HD-TMD to achieve the best vibration reduction rate, VFP-TMD faced the nonlinear problem caused by the large stroke of a pendulum system. Nevertheless, the performance balance design helped reduce this defect and provided impressive reduction capacity. Compared with the results of the optimal parameter formula, the peak damping rate and mean square error peak damping rate of the performance balance design lose only 3.19% and 0.74%.