The main objective of this study is to investigate the effectiveness of the Tuned Liqud Damper(TLD) in suppressing the dynamic response of cable-stayed bridges. The TLD is a new kind of damper, which relys upon the motion of shallow liquid in a rigid container for absorbing and dissipating the vibration energy. The effectiveness of TLD for reducing the dynamic response of the bridge deck and the pylon under turbulent wind is investigated, for several stages of construction, i.e. after construction and during erection. The analytical investigation shows that two TLD's which are mouted on the tops of the pylon and tuned to the first flexural mode of the bridge can reduce the response of the bridge deck and the pylon under turblent wind by 10-20%.