A multibeam radiator with each beam possessing independent polarization is developed by a single-feed holographic reflectarray (RA) antenna without using any optimization algorithms. Regardless of wave polarization, the relation between the electromagnetic properties of the antenna aperture (henceforth referred to as “hologram”) and impinging wave properties can be described by the holographic technique. For the practical implementation of such a hologram, we used a subwavelength metallic patch with anisotropic properties to satisfy the input admittance distribution of the hologram. In doing so, a fast numerical method, fundamentally inspired by the method of moments, is employed to calculate the input admittance of the element for all angles of incidence. This technique significantly speeds up the design process. Finally, as a typical case, a simple circularly polarized RA with four-beam radiation pattern was manufactured and tested at 13 GHz. The measured results showed that the aperture efficiency of 45.8%, cross-polarization discrimination of higher than 25 dB, 1 dB drop gain, 3 dB axial ratio bandwidths of 19.23% and 18.26%, sidelobe level of below −17 dB, and peak gain of around 19.43 dBi for each beam were obtained.