When floor vibration problems occur in existing buildings, TMD (tuned mass damper) can be a viable alternative to resolving the problem. Only when TMD has been exactly tuned to the natural frequency of the floor, it can control the vibration as intended in design. However, TMD gets inefficient in the situation where the natural frequency changes as a result of the uncontrollable variation of the floor mass weight. This physical phenomenon is often called as TMD-off-tuning. This study proposes asymmetric TMD for enhancing the robustness of floor vibration control against uncertain natural frequencies. The proposed TMD features two asymmetric linear springs such that the floor vibrational energy can be dissipated through both the translational and rotational motion. An easy-to-use graphical optimization method was developed in this study. The asymmetric TMD proposed outperformed in vibration control by 28% compared to that of conventional TMD. The robustness of asymmetric TMD of this study was two times higher than that of conventional TMD.