Millimeter-wave (mmWave) antennas are indispensable components in the fifth-generation (5G) wireless communication systems. With the inherent advantages of integration capability, substrate integrated waveguide (SIW) antenna is an excellent choice for applications in the mmWave frequency bands. However, reflection losses occur at dielectric-filled thin apertures of SIW antennas. These reflections can be overcome by impedance matching between the aperture and the free space. In this study, we introduce an mmWave SIW horn antenna having impedance matching transitions (IMTs) across the horn's aperture width. The designed antenna, operating in the 24-28 GHz band, is simulated with a full-wave analysis tool. The simulation results of the modified SIW horn have been confirmed by the experimental results and shown to be satisfactory. The IMTs result in an enhancement of the front-to-back ratio (FTBR). The modified SIW horn antenna with a novel printed transition achieves sidelobe levels (SLLs) of better than ?9 dB at 27 GHz, with an enhanced FTBR above 15 dB. In the 24?28 GHz band, the antenna has a reflection coefficient variation of better than ?10 dB.