An analytical model is developed based on linear potential flow theory and matching eigenfunction expansion technique to investigate the hydrodynamics of a two-dimensional floating structure. This structure is an integration system consisting of a breakwater and an oscillating buoy wave energy converter (WEC). It is constrained to heave motion, and linear power take-off (PTO) damping is used to calculate the absorbed power. The proposed model is verified against the published results. The proposed integrated structure is compared with the fixed structure and free heave-motion structure, respectively. The hydrodynamic properties of the integrated structure with the optimal PTO damping i.e., the transmission coefficient, reflection coefficient, capture width ratio (CWR), and heave response amplitude operator (RAO), are investigated. The effect of the PTO damping on the performance of the integrated system is also evaluated. Results indicate that with the proper adjustment of the PTO damping, the proposed integrated system can produce power efficiently. Meanwhile, the function of coastal protection can be compared with that of the fixed structure.