This paper presents a comparative study between the three-element tuned mass damper (T-TMD) and the conventional tuned mass damper (TMD) for vibration mitigation of offshore platforms subjected to ground excitations. The T-TMD is an enhanced configuration of the TMD, in which a viscous damper is connected in series with an additional spring. The equations of motion of offshore platforms equipped with the T-TMD are derived using the Lagrangian method. The constraint conditions of the T-TMD are analyzed to formulate the optimization problem, in which two objective functions are considered: maximizing vibration suppression efficiency and minimizing the device mass. The T-TMD parameters are optimized for a specific offshore platform based on these objectives. Numerical simulations demonstrate that the T-TMD provides superior performance and enhanced robustness compared to a conventional TMD of equal mass.