In this paper, the corrugated horn antenna used in the reflector feed horn of satellite is analyzed using the modal expansion method. The modal expansion method is represented by the summations of modals at each point so the exact prediction of field and phase patterns can be obtained. The least number of iterations to compute field patterns is proposed. By using this number. calculation of accurate near and far field patterns without comsuming a lot of computational effort is available. Three kinds of corrugated horn antenna is designed to verify the method and experimented. The VSWR of designed frequency is from 1.04 to 1.1. The input impedance is nearly matched to $50Omega$.