Conformal antenna can keep consistent with the shape of the carrier perfectly, which greatly saves the space of the carrier, so it is widely used in military, aerospace and other fields. In this paper, a cylindrical conformal circular polarization Fabry-Perot resonator antenna is designed, and the adverse effect of conformal on antenna gain is overcome by transmission phase compensation. Firstly, a linear to circular polarization conversion metasurface with adjustable transmission phase is designed. The main reason for choosing the metasurface here is to take advantage of its excellent electromagnetic control ability. The metal structures of the metasurface are printed on the ultra-thin dielectric plates, and then attached to the support structure machined by 3D printing, so as to achieve the conformal design of the metasurface. Secondly, the proposed metasurface is used as the superstructure and is combined with a conformal feed to form a cylindrical conformal circularly polarized Fabry Perot resonator antenna. The conformal feed is a patch antenna which is conformal designed in the same way as the metasurface. The conformal feeder is placed under the conformal metasurface to ensure that the electromagnetic wave radiated by the feeder can enter the resonant cavity composed of the feeder and the metasurface. The curvature of the cylindrical conformal of feed and metasurface is the same, which can ensure the high unity of the different positions in the resonator. Next, by adjusting the transmission phase of the unit on the metaurface, the phase compensation of the transmitted electromagnetic wave is realized, so that the electromagnetic wave radiated by the conformal antenna still presents the characteristic of plane wave. Finally, the conformal Fabry-Perot resonator antenna obtains the same high-gain radiation characteristics as the planar resonator antenna. The designed antenna achieves a maximum gain of 13.1dBic at 10 GHz. The size of the antenna is 2.9λ × 2.9λ, so the aperture efficiency is about 19.9 %. The antenna proposed in this paper overcomes the influence of conformal design on the gain of the antenna, so that it can be conformal on the surface of a cylindrical object and obtain better gain characteristics.