The hydrodynamic performance of a bottom-hinged flap wave energy converter (WEC) is investigated through a frequency domain numerical model. The numerical model is verified through a two-dimensional analytic solution, as well as the qualitative analysis on the dynamic response of avibrating system. The concept of “optimum density” of the bottom-hinged flap is proposed, and its analytic expression is derived as well. The frequency interval in which the optimum density exists is also obtained. The analytic expression of the optimum linear damping coefficient is obtained by a bottom-hinged WEC. Some basic dynamic properties involving natural period, excitation moment, pitch amplitude, and optimum damping coefficient are analyzed and discussed in detail. In addition, this paper highlights the analysis of effects on the conversion performance of the device exerted by some important parameters. The results indicate that “the optimum linear damping period of 5.0 s” is the most ideal option in the short wave sea states with the wave period below 6.0 s. Shallow water depth, large flap thickness and low flap density are advised in the practical design of the device in short wave sea states in order to maximize power capture. In the sea state with water depth of 5.0 m and wave period of 5.0 s, the results of parametric optimization suggest a flap with the width of 8.0 m, thickness of 1.6 m, and with the density as little as possible when the optimum power take-off (PTO) damping coefficient is adopted.