Jacket structures are one of the most important offshore structures for extracting oil and gas. The fatigue life is affected due to the continuous dynamic wave force experienced by the structure. Generally, the structure is designed so that the dynamic response is small, which increases the cost. So, controlling its response is a good alternative to increase its life span. In this work, a simplified jacket structure under a random sea state is controlled for its response using a tuned liquid column ball gas damper (TLCBGD). The jacket structure in a water depth of 60m is modeled in a surge degree of freedom. The parameters of TLCBGD are optimized using a genetic algorithm for achieving better control in response quantities. For the analysis purpose, the wave is considered stochastic and presented by Pierson–Moskowitz (PM) spectrum of significant wave height 10m. In such a case, the jacket structure response can be presented using the root mean square (RMS) values obtained from the Lyapunov technique. Based on the random vibration analysis theory, the Lyapunov method can be employed to obtain the RMS of the system driven directly without solving the governing differential equation. This method requires the system to be driven by white noise. So, in this study, filters are developed to get the required narrow banded ocean spectrum. It is noticed that the response quantity is highly sensitive to the filter parameters. This is because a slight change in excitation parameters and a change in filter parameters near the system’s natural frequency affect the response significantly. Further, it is seen that the use of the genetic algorithm for tuning the TLCBGD gives very good control on the response quantity of the jacket structure.