In a mid-story isolated building, the isolation system is incorporated into the mid-story rather than the base of the building. The effectiveness of mid-story isolation design in reducing seismic demands on the superstructure above the isolation system has been verified in many researches. It was also disclosed, however, that the significant seismic responses at the substructure below the isolation system and a significant phase lag between the seismic responses of the superstructure and substructure should be paid more attention, especially when the isolation system is installed at a higher story or the substructure is not sufficiently stiff. On the contrary, observed from the past researches and practical applications, it was evident that the adoption of tuned mass damper (TMD) design can effectively enhance the seismic-resistant capability, in addition to the wind-resistant capability, of a building, in particular of a high-rise building. Generally, the additional tuned absorber mass is much smaller than the building itself mass and is installed on the top of the building, namely the main structure or the substructure thereafter. Although an increase of the tuned absorber mass results in a better dynamic control performance for the main structure, it also leads to an immense increase of the damping demand for TMD design. Therefore, in this thesis, the feasibility of the incorporation of the TMD design concept into a mid-story isolated building, namely building mass damper (BMD) design thereafter, is numerically studied. The stiffness and damping of the BMD system can be provided by the mid-story isolation system composed of seismic isolation bearings and viscous dampers. Most importantly, the superstructure can serve as a tuned absorber mass such that the size limitation of the conventional TMD design method can be overcome. A simplified three-lumped-mass structural model in which the flexibility effects of the superstructure and substructure are comprehensively considered is used to represent the dynamic characteristics and seismic behavior of a building with BMD design. The objective function to determine the optimum BMD design parameters is that, the damping ratios of the three translation modes of the simplified structural model are essential and should be very close. The influences of the interested parameters of the simplified structural model on BMD design are thoroughly investigated through a sensitive analysis manner. Based on the sensitive analysis results, it is seen that the BMD design concept is doable with a very acceptable damping ratio demand. Furthermore, the suitable occasions to apply mid-story isolation design, TMD design and BMD design are defined explicitly. A preliminary BMD design procedure with an iteration process is also proposed. Both a scaled down test model and a practical structural model (i.e. National Center for Research on Earthquake Engineering) with different design methods (including conventional design, mid-story isolation design, TMD design and BMD design) are applied to the numerical study. The numerical study results indicate that the BMD design method, which possesses two predominant modes, is really effective for the seismic protection of both the superstructure (tuned mass structure) and substructure (main structure).