We propose broadbeam geodesic H-plane horn antennas, potentially useful as simple primary feeds for reflectors. Since H-plane horn antennas are implemented in a structure similar to the parallel-plate waveguide, we show that a numerically efficient ray-tracing model can be used to describe wave propagation through them. Using the efficient ray-tracing tool, we optimize three different height profiles to obtain broad beams with different half-power beamwidths at the central operating frequency of 30 GHz. All implemented structures have beamwidths larger than those of a planar reference counterpart.