H∞ control of the critical modes of vibration of an offshore platform under ice loads was studied.The control was applied to a platform via an active tuned mass damper (AMD) located at the top of the platform. An algorithm combining the H∞ method together with balanced reduction scheme in modal space was used for control design. The solution for iceinduced vibration response of the system was derived in terms of pseudoexcitation method. With the derived solution, extensive parametric studies can be carried out. The optimal parameters of H∞ controllers for achieving the maximum vibration response reduction of the platform can be identified. The effectiveness of H∞ controllers for this particular application is evaluated.The results show that the iceinduced vibration response of the platform can be considerably reduced if the parameters of H∞ controllers are selected appropriately.