Excessive acceleration experienced at the top floors in a building during wind storms affect the serviceability of the building with respect to occupant comfort and discomfort. Tuned liquid damper (TLD) and multiple tuned liquid damper (MTLD), which are passive control devices consisting of a rigid tank filled with liquid, are used to suppress vibration of structures. These TLD and MTLD offer several potential advantages-low costs, easy installation in existing structures and effectiveness even for small-amplitude vibrations. This study carries out a theoretical estimation of the most effective damping ratios that can be achieved by TLD and MTLD. Damping by TLD an MTLD reduced the frequency response of high-rise buildings by approximately 40% in urban and suburban areas.