Abstract: To generate a far field pattern of satellite mounted antenna matching the coverage area, and obtain the high gain and the cross polarization isolation, the application of Minimax method in the design of a single offset shaped reflector antenna represented by the Jacobi-Bessel function is addressed. The expansion coefficients of the surface are set as the parameters to be optimized and a combined method of physical optics(PO) and physical theory of diffraction(PTD) is used to calculate the far field pattern. The gain and the cross polarization isolation are regarded as the optimization aims. In order to avoid the creation of un-realizable reflector shapes, a limit is added to the deviation in the z-direction from the original paraboloid. Finally, the contoured beam covering the Brazilian territory is optimized. The results show that the copolar gain is above 28.5dBi and the cross polarization isolation is better than 21dB in all coverage areas.