A three-dimensional fixed offshore platform in deep water modeled by the finite element method is studied in this paper. Analysis of the dynamic response of the MDOF structure is realized taking the non-linearity of the wave drag force and the wave-structure interaction into account. The structural response statistics, which have Gaussian distributions, are used to evaluate the vibration effect of the structure without TMD and with TMD. And an optimal method to design TMD controlling the first mode of the multi-mode structure is proposed. Moreover, the probabilities of occurrence of sea states at the platform site are considered for prediction of the long-term effect of a TMD. Simulation results demonstrate that the long-term effect of a well-designed TMD is good and the practical use is possible due to the good stability of its optimal parameters under different sea states.