To address the unstable motion of a tension leg platform (TLP) for floating wind turbines in various sea conditions, an improved method of incorporating a tuned liquid multi-column damper (TLMCD) into the TLP foundation is proposed. In order to evaluate the control effect of TLMCD on the motion response of the floating foundation, a multiphase flow solver based on a viscous flow CFD method and overlapping grid technique is applied to model the coupled multi-body dynamics interaction problem involving liquid tanks, waves, and a spring mooring system. This method has been proven to accurately capture the high-frequency motions of the structure and account for complex viscous interferences affecting the geometric motions. Additionally, the volume of fluid (VOF) method and the first-order linear superposition method are used to model the focused wave, enabling a simulation of the effects of transient wave loads on the floating foundation. The results show that the tuned damping effect of TLMCD on the TLP is mainly in the pitch motion, with the maximum pitch amplitude control volume ratio of TLMCD reaching up to 86% and the maximum surge amplitude control volume ratio of TLMCD reaching up to 25.2% under the operating conditions. These findings highlight the potential for additional research on and implementation of TLMCD technology.