The proposed design approach improves the circularly polarized Fabry-Perot cavity antenna (CP-FPCA) by increasing gain and sidelobe suppression (SLS) while reducing the axial ratio (AR) and cross-polarization levels. Conventional CP-FPC antennas have a high AR due to the lack of independent control over circular polarization conditions. The solution proposes a double-layered circularly polarized partially reflecting surface (CP-PRS) that independently controls the circular polarization conditions at the design frequency f0 (10 GHz) for equal magnitudes and at a ±90° phase difference between orthogonal components of the transmitted waves. The PRS and artificial magnetic conductor (AMC) unit cells are employed to satisfy Trentini’s beamforming condition, leading to increased gain and SLS and lowered AR and cross-polarization levels. Consequently, the proposed CP-FPCA provides a 15.4 dBi high gain with 25.3% aperture efficiency and more than 23.5 dB high SLS in each plane. Moreover, it achieves an AR lowered by 0.12 dB and a cross-polarization level below −42 dB. A strong correlation between the simulations and experiments proves the practicality of our proposal.