Parameter optimization for tuned liquid column dampers (TLCD), a class of passive structural control, have been previously proposed in the literature for reducing vibration in wind turbines, and several other applications. However, most of the available work consider the wind excitation as either a deterministic harmonic load or random load with white noise spectra. In this paper, a global direct search optimization algorithm to reduce vibration of a tuned liquid column damper (TLCD), a class of passive structural control device, is presented. The objective is to find optimized parameters for the TLCD under stochastic load from different wind power spectral density. A verification is made considering the analytical solution of undamped primary system under white noise excitation by comparing with result from the literature. Finally, it is shown that different wind profiles can significantly affect the optimum TLCD parameters.