A Gaussian beam-mode analysis of the operation of a corrugated feed horn is presented. The electric field over the aperture is expanded in terms of a set of Gaussian-Laguerre modes. These modes are solutions to the wave equation, in a paraxial approximation, and propagate from the aperture in a simple and well defined way. The antenna pattern of the horn in any plane in the near or far field is found by summing the contributions from the modes. This process is computationally faster than the standard Fresnel expansion, and provides a new insight into the operation of feed horns. It is particularly appropriate when the horn feeds a quasioptical system. Almost 98% of the power is carried in the fundamental Gaussian mode. To illustrate the application of the method, an analytical expression for the position of the phase centre is derived and the coupling between two horns is calculated.