By flaring a dielectric waveguide in the H-plane, an H-plane dielectric horn is formed, which could be directly excited by an SIW feed. However, matching and radiation performances are poor due to the thinness of the substrate. To improve these performances, some periodic parallel strips are printed both on the top and bottom planes of the dielectric horn. These strips guide and leak the electromagnetic waves gradually along the horn, finally enhancing the end-fire radiation both in H-plane and E-plane. Moreover, they increase the impedance bandwidth up to 40% in Ka-band, and improve the realized gain by more than 2 dB. Indeed, a gain of 14.9 dBi is achieved at the center frequency, with a front-to-back ratio of 33.8 dB, and a side-lobe level of -22.9 dB in the H-plane. With these quite impressive performances, the proposed leaky-wave dielectric horn antenna is very compact, low cost, and easily integrated.