This paper presents an H-plane SIW horn antenna whose directivity is enhanced using holey unit cells along the horn flaring. By wisely drilling the horn antenna, it is possible to reduce the phase error in the aperture which is a common problem in horn antennas if the optimum dimensions are not employed. An analysis of the distribution of the unit cells along the horn antenna has been carried out to achieve the desired equivalent refractive indices. By changing the hole radius, different equivalent refractive indices can be tuned with a wideband performance. This fact enables the implementation of a collimation zone inside the horn antenna which transforms the pseudo-circular wavefront into a quasi-planar one in the radiating aperture. The produced directivity is similar to the horn antenna with the optimum dimensions but a longitudinal reduction of 53.7% and a higher realized gain are achieved. A holey SIW horn antenna is designed and manufactured. The measured results show an impedance bandwidth performance below -10 dB from 34.3 GHz to 44.5 GHz (25.9%) with a realized gain above 10 dBi. The gain difference regarding a SIW horn antenna without the collimation zone is about 2-3 dBi in the operating frequency range.