In this paper, we have designed the elliptical dual offset gregorian antenna which can use Ka band earth station antennas in the fixed-satellite service. The structure of antenna is increasing the antenna gain by decreasing blockage areas and decreasing wind effects by shortening height of the antenna. The corrugate horn antenna for this antenna has symmetric radiation patterns and low side lobe levels that can meet ITU-R envelope. The distribution of electric field on a aperture of main reflector is calculated by an ray-tracing method that use the radiation pattern of the feed horn. The final geometric of antena is decided by choosing the distribution that comply with antenna requirement. The FEKO analysed electrical performance of this antenna. The fabricated antenna has 45.0dBi(@30.0GHz)/41.7dBi(@20.2GHz), high efficiency and low side lobe level that meet ITU-R S. 580-6 envelope.