Tuned mass dampers (TMDs) are well recognized as an effective technology for mitigating structural vibration caused by wind loads. Therefore, some researchers have advocated applying TMDs for the vibration mitigation of structures subjected to earthquakes. Nevertheless, the seismic performance of a conventional TMD may not be as effective as expected because the frequency content and magnitude of an earthquake usually fluctuate and are far more complex than wind loads. To resolve this problem, the leverage-type stiffness controllable mass damper (LSCMD), a semi-active mass damper, is proposed in this paper. The LSCMD has a lever arm with a movable pivot, allowing it to control the damper stiffness and restoring force in real time by adjusting the pivot position. To evaluate the control effectiveness of the LSCMD, the seismic responses of a structural system equipped with the LSCMD were simulated and compared with those of the same structure controlled by two optimally designed passive TMDs and a hybrid mass damper (HMD) with the same control law as that of the LSCMD. The results of the simulation demonstrate that the control performance of the LSCMD system can be enhanced by varying the LSCMD stiffness. Although the LSCMD and HMD are equally effective in suppressing the maximum responses of the structure, the former requires less control energy. This indicates that the proposed LSCMD is more desirable when the damper installation space and energy consumption are major concerns.