A design method for horn antennas in which high efficiency and low cross polarization can be realized at the same time is described. In the design, the excitation coefficients for the modes at the antenna aperture are derived in order to realize these characteristics. The antenna taper shape is determined by controlling multiple modes by optimization in order to obtain these coefficients on the horn aperture. The effectiveness of the design method is verified by measurements of the radiation patterns of the tested antenna in the X band and by numerical results. It is also confirmed that a high efficiency, exceeding 80%, and a low cross polarization of less than -30 dB can be obtained. It is demonstrated that a highly efficient horn antenna with a low cross polarization, not previously available, has been realized.