A linear open-close loop control strategy is presented for controlling the response of the offshore articulated leg platform (ALP) in which the performance function involves structural acceleration in addition to the usual state variables, i.e., angular displacement and velocity of the tower, and the sea surface elevation and its variables. The weightage of the structural acceleration in the performance function is regulated by incorporating an acceleration weighting factor. The performance function is minimized to obtain the control law using the well-known Ricatti equation. The control law thus achieved is implemented to control the peak responses of a 180.5-m tall ALP under a random sea state, using an iterative frequency domain technique to consider all the nonlinearities present in the system. The efficiency of the proposed strategy is investigated through an extensive parametric study.