In this inquisition, a passive damper namely Stockbridge Damper (SBD) has been introduced to the field of vibration control of Offshore Wind Turbine (OWT) to reduce the earthquake excitations. The dynamic responses of the structure have been analyzed for three recorded earthquakes and the responses have been assessed. To find an optimum SBD, the parameters of damper have been optimized using Response Surface Methodology (RSM) based on Box-Behnken Design (BBD) and Particle Swarm Optimization (PSO). The influence of the design variables of SBD such as the diameter of messenger cable, the length of messenger cable and logarithmic decrement of the damping has been investigated through response variables such as maximum displacement, RMS displacement and frequency amplitude of structure under an artificially generated white noise. After that, the structure with optimized and non-optimized damper has been analyzed with under the same earthquakes. Moreover, the comparative results show that the structure with optimized damper is 11.78%, 18.71%, 11.6% and 7.77%, 7.01%, 10.23% more effective than the structure with non-optimized damper with respect to the displacement and frequency response under the earthquakes. The results show that the SBD can obviously affect the characteristics of the vibration of the OWT and RSM based on BBD and PSO approach can provide an optimum damper.