A vector form intrinsic finite element method ( plane frame element ) is developed and applied to study the dynamic responses of offshore template platform under wave force. The horziontal, vertical and rotational motions at each node in the finite element model also were analyzed by the developed solution procedure of offshore structures. Besides, this paper also discussed the application of viscoelastic dampers on the offshore structures. A design for the dampers incorporated in the template structure were presented, and dynamic analyses were carried out to observe the effect of the vibration mitigation on the structures .