This work seeks a novel design for a compact leaky-wave array antenna for high-power microwave (HPM) applications. The leaky-wave antenna is made of a rectangular waveguide with closely spaced non-resonant slots in the broad-wall of the waveguide. By this means, more slots can be set within a unit length and less energy will radiate from each slot, then higher power-handling capacity can be achieved. An L-band leaky-wave waveguide antenna centered at 1.57 GHz is designed and experimentally studied. The results show that the radiation efficiency of the antenna is 97% and the power-handling capacity of a single waveguide exceeds 1.3 GW. In addition, a 5-waveguide array antenna is also designed. The antenna array has an aperture efficiency of 76.6% and the beam scanning range can reach ±40° in H-plane, which would be suitable for many HPM applications.