This paper presents a design of a tuned liquid mass damper(TLMD) for controlling bi-directional response of high-rise building structure subjected to windload. The proposed damper behaves as a tuned mass damper(TMD) of which mass is regarded as the mass of a tuned liquid column damper(TLCD) and the case wall of the TLCD itself in one direction and the TLCD in the other direction. Because the proposed device has coupled design parameter along two orthogonal directions, it is very important to select designing components by optimal fine tuning. In the designing TLMD, for easy maintenance, the rubber-bearing with small springs was applied in TMD direction. In this study, the Songdo New City Tower 1A in Korea, which has been designed and constructed two TLCDs in order to control bi-directional response, was chosen as the model building structure. The results of rotation test proved the effectiveness of bi-directional behavior of TLMD.