A new method of designing horn-fed frequency scanning holographic antenna is proposed. The artificial surface design of holographic antenna is based on generalized law of reflection. The input admittance is utilized to construct the interference pattern of the surface which is intervened by the excitation wave and the required radiation wave. The scalar admittance unit cell which is composed of sub-wavelength metallic patch on grounded dielectric substrate is implemented to design artificial surface, and the simulation results are just as expected that the antenna can scan the beam as the frequency changes. Furthermore, a cross shaped patch printed on grounded dielectric unit cells is used to reduce the designing complexity of tensor admittance surface. At last, a frequency scanning holographic antenna with tensor admittance surface with ability of changing linear polarization excitation wave to left-hand circular polarization (LCP) radiation wave is designed and fabricated. The full-wave simulation and experimental results show well agreement and confirm the method proposed.