The radiation characteristics of the conical corrugated feed horn are analyzed by the Gaussian beam mode theory. the electric field over the aperture can be expanded in terms of a set of Gaussian-Laguerre modes. It is proved that these modes are the solutions of the wave epuations for the paraxial approximation. A method, using the sum of the mode expansion coefficients instead of calculation only the fundamental mode, is presented in order to reduce the radiation pattern error. For illustrative examples, the radiation patterns of the corrugated horn antenna operting over C, Ku, and mm-wave band are calculated. Our results agree well with the results obtained by the vector potential method over each band, and also agree well with the measured value at 6.175GHz.