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This paper investigates the performance of a rectangular tuned liquid damper (TLD) used to suppress a structure’s roll motion. In the theoretical analysis, the potential theory is employed to derive the equation of motion for the structure’s inclination angle and the modal equations of motion for the lowest three sloshing modes, considering the nonlinearity of sloshing. Then, van der Pol’s method is applied to the resulting equations to derive the expressions for the frequency response curves. It is found from the frequency response curves that the performance of the TLD depends significantly on the distance between the TLD and the center of the structure. Experiments were also conducted and confirmed the validity of the theoretical analysis.