Base isolation can achieve a reduction in floor acceleration and inter-story drift. However, it may suffer from excessive displacements under near-fault and far-field earthquakes. To improve the aseismic performance of passive base-isolated structures, in this paper, a semi-active tuned mass damper (STMD) with variable stiffness and damping is presented. A combined control algorithm based on output signals only is developed for the STMD first. Then, the STMD is applied to an eight-story linear base-isolated structure and also a nonlinear one. As for the linear model, which represents a theoretical benchmark, an optimized passive TMD (PTMD) is used for comparison. As for the nonlinear model, lead rubber bearing (LRB) is considered and simulated using the well-known Bouc-Wen model. Eight earthquakes with different spectral characteristics and peak ground amplitudes are chosen, and two PTMDs are optimized for comparison, while one is tuned to the pre-yield period of the base-isolated model and the other is tuned to the post-yield period of the base-isolated model. Numerical results show that, generally, STMD has the best control effect in both linear and nonlinear models. For displacement responses, because STMD can vary its stiffness and damping, it can mitigate the structural first-mode response effectively, and can achieve both top story and isolated level responses reduction. As for acceleration responses of the top story, STMD achieves excellent performance in the structural second-mode acceleration response mitigation. Therefore, STMD can improve both displacement and acceleration performances of both linear and nonlinear base-isolated structures effectively.