In a horn antenna apparatus for use in an antenna system for radar, some of the excited radio waves in a TE11 mode in a radio-wave input portion 1 are converted to those in a higher mode in a waveguide portion 5. As the inclination of a line of intersection S of the waveguide portion 5 is not fixed but continuously varied, the higher mode such as a TM11 mode and TE12 mode and the like is excited everywhere in the direction of the axis Z of the waveguide portion 5. Then the configuration of the line of intersection is determined so that an amplitude and a phase as the generated quantity of higher mode such as the TM11 mode generated in the waveguide portion 5 conform to desired values with respect to each higher mode.