Linearly flaring horn antennas typically suffer from low aperture efficiency, especially for large apertures. While spline horns can improve the aperture efficiency, this is at the cost of increased and more complex profile. This paper introduces a novel compact horn antenna fed by leaky waves from the horn arms, which presents a good aperture efficiency and geometrical simplicity. The proposed H-plane high gain horn consists of two leaky-wave waveguides. To demonstrate the idea, two leaky-wave waveguides are implemented in the technology of substrate integrated waveguide (SIW). The horn flaring angle is as large as 110° in this example. By combining the two leaky-wave radiation, a linearly phased wave front is formed. As a result, a high antenna gain of 14.3 dBi at 27 GHz is achieved, with the beamwidth of 6° and side-lobe level of -18 dB. There is no constrains on the horn flaring angles and radiation aperture sizes. This compact leaky-wave SIW horn antenna is very promising for the application as high gain antennas and feed.