In this study, we propose a new seismic control device, tuned viscous mass damper (TVMD), for building systems. We give a detailed description of an apparent mass amplifier using a ball-screw mechanism, which is one of the most important components for realizing the new device. We also derive a closed-form solution of an optimum seismic control design for a single-degree-of-freedom structure subjected to harmonic excitation. The performance of the new device is compared with those of the conventional viscous damper and viscous mass damper systems. The vibration control system using the TVMD is shown to be the most effective for linear structural systems with dampers having the same additional damping coefficient. The effectiveness of the TVMD for seismic excitation is verified by analyses and shake table tests with a small-scale TVMD.