A flap-type wave energy converter (WEC) is combined with a nearshore breakwater to expand the application of WECs both economically and environmentally. Based on the linear potential theory, an eigenfunction expansion solution is developed for a periodic row of bottom-hinged flap-type WECs exposed to normal waves. Additionally, the viscous effect is considered using the ship rolling solution method with a viscous damping term included in the equation of motion, and the viscous damping expression is also described. The proposed solution is verified by comparison with published literatures. The results including the wave energy conversion efficiency, the reflected and transmitted proportion of the incident wave energy are presented for a range of wave periods and geometric ratios. It is demonstrated that better wave protection effects can be attained with smaller gaps between the WECs, where the transmitted proportion of the incident wave energy is lower. An optimal geometric ratio thus exists for a given wave power absorption and a specific wave period.