Abstract: To make the far field pattern of the antenna mounted on satellite to match the coverage area, and obtain the high gain and the finer cross polarization isolation, the application of the improved real coded genetic algorithm in the design of a single offset shaped reflector antenna is addressed. In the optimization process, the gain and the cross polarization isolation are regarded as the optimization targets and the fitness function is constructed based on the goal programming. To guarantee the diversity of the chromosome, a hybrid method composed of difference evolution manner, insert/extrapolate and gene exchange is used to generate the new individuals and the adaptive aberrance probability is adopted. Finally, the numerical simulation results of a shaped reflector antenna at Kuband are presented. The results show demonstrate that the pattern of the far field matches the shape of the coverage area very well and all the parameters are consistent with the targets of design, which fully validate the feasibility and validity of the proposed procedure.