The mitigation of structure vibration subjected to strong wind by using a tuned mass damper (TMD) has been applied practically and is demonstrated be an effective technology. However, a TMD with fixed design parameters may not alleviate the responses of structure subjected seismic loadings because the frequency content of earthquake is complex and unpredictable. To solve this problem, a semi-active mass damper (SAMD) whose designed parameters can be adjusted according to structural responses through the application of appropriate control force to the original passive device has been proposed in recent years. A leverage-type stiffness controllable mass damper (LSCMD) is adopted in this study to improve the performance of a conventional TMD. Based on the discrete-time optimal LQR output feedback control algorithm, the control performance of the LSCMD can be improved as deigned. Therefore, the target pivot position of the leverage mechanism can be determined in real time to provide the controllable stiffness for the LSCMD. To demonstrate the theory and feasibility of the LSCMD, a shaking table test is also conducted. From the comparisons of experimental and numerical results, the structural responses subjected to white noise earthquake and Chi-Chi earthquake can be suppressed with smaller stroke when equipped with LSCMD.