An earlier numerical study of a single-degree-of-freedom (SDOF) structure, rigidly supporting a tuned liquid damper (TLD) and subjected to broad-band ground motions, showed that a TLD had to be properly designed for effectively reducing the structure’s response. In this paper a comprehensive study of the effect of various ground motion parameters on the ability of a TLD to reduce structural response for earthquake base motions is presented. The frequency content and bandwidth of the ground motion do not significantly affect the effectiveness of the TLD. Since the TLD is a nonlinear system, its effectiveness increases with increasing intensity of ground motion. Furthermore, as it behaves as a viscous damper, it cannot reduce the response in the first few cycles of vibration. Therefore, it is more effective for far-field ground motions, where the strong motion and consequently the peak response of the structure occur after the first few cycles of vibration.