The electromagnetic field phase distribution in horns' apertures is affected by the horn flaring and is usually not uniform, resulting in a lower antenna gain. This paper presents an H-plane SIW horn antenna with the aperture phase corrected by some gaps on the H-plane metallic walls, to enhance the antenna gain. To achieve a better radiation and impedance matching, some planar tapered-ladder transitions are printed just after the horn aperture. Simulations in HFSS software, including a probe excitation, have shown good phase correction and hence increased gain, while also providing good impedance matching. The designed compact Ka-band antenna achieves an enhanced gain of 10.1 dBi at 34 GHz, and an impedance bandwidth of 4.33 GHz.