Starting from the geometrical parameters of the feed and the desired gain of the Cassegrain antenna, a method to determine the design starting parameters for a high-power offset Cassegrain antennas is discussed. Then, by numerically solving the equations governing the antenna geometry, a set of design curves are obtained, with which the structure of the antenna can be determined by trading off the electrical and geometrical system requirements. The method presented can be applied to both high or low gain feeds for constructing a high power microwave electromagnetic environment, where complex electronic systems can be tested. For linearly polarized feeds with high gain, the structure parameters of antenna with zero cross polarization can be obtained, which is equal to the design results of Brown and Prata (see IEEE Trans. Antennas Propagat., vol.42, no.8, p.1145-53, 1994).