A new Fabry-Perot cavity antenna simultaneously producing a high-gain and a wide beamwidth is proposed. To get increased antenna gain and reduced back radiation, all the openings of the antenna are enclosed with metallic walls, and to obtain a broader beamwidth, the antenna has been fabricated in a rectangular shape, with an aspect ratio of about 3.5:1. In addition we propose a new method to more accurately predict the frequency of the maximum gain by considering a resonance mode of the cavity enclosed by metallic walls. Good agreement between the prediction and measurement results ensures the validity of the new design approach to provide easy control of gain and beamwidth at the same time.