A Fabry-Perot (FP) antenna with high gain-bandwidth product (GBP) and wideband radar cross section (RCS) reduction is proposed using an embedded chessboard polarization conversion metasurface (CPCM). A polarization conversion metasurface (PCM) unit and its mirror unit are etched on both sides of a dielectric substrate with chessboard arrangement to form a CPCM. The in-band and out-of-band low-RCS features of the FP antenna are realized by destructive interference, and the high GBP is attributed to the FP resonant cavity. Moreover, an additional small CPCM designed for another PCM unit is embedded into the original CPCM to construct an embedded CPCM, which helps to improve in-band RCS reduction and has a positive effect on gain enhancement and 10-dB impedance bandwidth. The measured results show that the FP antenna with embedded CPCM has a 10-dB return-loss bandwidth of 8.48-12.21 GHz (36.1%), a GBP of 1338, a 3-dB gain bandwidth of 8.9-11.5 GHz (25.5%) and a maximum realized gain of 17.2 dBi. Meanwhile, the measured RCS reduction band covers 8-26 GHz (105.9%) with a peak RCS reduction of 21.2 dB at 9.4 GHz.