We obtained the predicted and measured results for the reflection coefficient and radiation pattern of Ka-band (20- GHz) corrugated horn, which is usually used for feeder of reflector antenna for satellite communication, using suface impedance condition. In order to predict the reture losses of corrugated horn, we analyzed propagation constant of hybrid mode in the corrugated waveguide and then obtained the total reflection coefficient using the circuti theory of multi-step transformer. We also got the radiation pattern of corrugated horn with small flare angle, considering the phase deviation and integrate transverse field on aperture. A test model of corrugated horn antenna for Ka-band designed using theory and program displayed performance and the results agree with the theoretical prediction.