Abstract: A dual-band coaxial horn feed applied in the field high power microwaves is proposed with theoretical analysis and numerical simulation. It is fed by circular waveguide with horizontal corrugations at 4.15 GHz and by coaxial waveguide at 1.75 GHz. Unwanted higher order modes at low frequency can be limited effectively by reducing the outer radius of the coaxial waveguide, and vertical corrugations located at the coaxial waveguide can improve radiation characteristics at high frequency effectively at the same time. With mode matching theory determining the scatter matrix of the feed, the theoretical results and simulation results agree well with each other. It is shown that the dual-band horn feed is compact with low side lobes and azimuthally symmetrical radiation patterns.