Tuned viscous mass damper （TVMD） is widely recognized as one of the promising inerter-based devices. This study fo? cused on investigation of the effective damping ratio enhancement effect and optimal design of TVMD for building structures under seismic excitations. The TVMD control performance for the structural inherent damping energy dissipation power was regarded as an effective damping ratio added to the primary structure. Further， a theoretical expression of the TVMD effective damping ratio was derived based on the random vibration theory. To make the application of TVMD more valuable， TVMD was expected to ob? tain a larger effective damping ratio compared to the viscous damper （VD） with the same damping coefficient， which was defined as the effective damping ratio enhancement effect. The effective damping ratio enhancement factor was introduced for the quantita? tive evaluation of the enhancement effect on the damping ratio. Both the effective damping ratio and the effective damping ratio en? hancement factor were considered as optimization objectives， and a closed-form solution of TVMD optimum design parameters was therefore proposed. Analysis results showed that the proposed closed-form solution had an excellent applicability and stability. The TVMD mass ratio and damping ratio were recommended to be less than 0.3 and 0.1， respectively， for the sake of the best effi? ciency of the damping ratio enhancement effect. A 7-story steel benchmark model was taken as an engineering example to illustrate the TVMD optimal design process and to verify the validity and superiority of the proposed closed-form solution. It was found that the deformation of the damping element for TVMD designed by the proposed closed-form solution was amplified remarkably， dem? onstrating the desired effective damping ratio enhancement effect. Most importantly， compared to the traditional closed-form solu? tion， the best advantage of the proposed closed-form solution is to ensure that TVMD control performance is better than VD with the same damping coefficient， regardless of control efficiency problem.