A bottom-fixed flap-type pitching wave energy absorber which operates near-shore is studied. The design consists of an arm hinged on the sea bed and supporting a flap. The flap has an elliptical cross section spanning vertically from the free surface to about one third of the water depth. A mechanism is provided which allows the flap to be fixed at a variable angle relative to the supporting arm. Such mechanism is here proposed as a means of broadening the absorption bandwidth and avoiding large forces while still absorbing power. The variations of maximum absorbed power and reaction force with wave frequency are obtained for different flap widths and angles and for different angular displacement limits, on the basis of linear potential theory. Further analysis on the absorber with a selected flap width is then presented and its performance is shown to be promising.