In this paper, a novel boundary control method is investigated to suppress the vertical vibration of a very large floating structure (VLFS) with regular waves. The VLFS can be described as a distributed parameter system with partial differential equation (PDE). The proposed boundary controllers are developed based on Lyapunov's direct method to act on the upstream and downstream ends of the VLFS, respectively. Along with the suitable choice of control parameters, the proposed controllers could stabilize the vertical vibration of the VLFS subjected to regular waves. This study verifies the effectiveness of the proposed control methods to the VLFS. Then, the effects of wave amplitude and bending rigidity on the hydroelastic response of the VLFS are investigated.