In this study, the performances of a passive tuned mass damper (TMD) and a semi-active TMD (STMD) were evaluated in terms of seismic response control of elastic and inelastic structures under seismic loads. First, elastic displacement spectra were obtained for damped structures with a passive TMD and with a STMD proposed in this study. The displacement spectra confirmed that the STMD provided much better control performance than passive TMD and the STMD had less stroke requirement. Also, the robustness of the TMD was evaluated by off-tuning the frequency of the TMD to that of the structure. Finally, numerical analyses were conducted for an inelastic structure of hysteresis described by the Bouc-Wen model. The results indicated that the performance of the passive TMD whose design parameters were optimized for an elastic structure considerably deteriorated when the hysteretic portion of the structural responses increased, and that the STMD showed about 15-40% more response reduction than the TMD.