In this study, a procedure to design an optimal LCVA that maximizes the equivalent damping ratio added to the primary structure subjected to along-wind excitation is proposed. That design procedure does not only consider the natural frequency and damping ratio of the LCVA, but also the proportion of the U-shaped liquid, which is closely related to the participation ratio of the liquid mass in inertial force. In addition, constraints to ensure the U-shape of the liquid are considered in the design process, so that suboptimal solutions that violate the optimal tuning law partly are adopted as a candidate of the optimal LCVA. The proposed design procedure of the LCVA is applied to the control of the 76-story benchmark building, and the optimal proportions of the liquid shape under various design conditions are compared.