The remaining challenges, confronting the limited output peak power level of high-power microwave (HPM) sources, stimulate the development of power combining system. This paper reports the design methods and numerical results for a kind of dual-band incoherent power combining architecture applied in HPM. It is particularly effective to radiate dual-band microwave simultaneously, generated by a coaxial dual-band HPM source or two separate HPM sources of different bands. Two types of mode conversion structures, i.e., a dual-band feed line with co-aligned ports and a dual-band feed line with off-aligned ports, are proposed, where coaxial output port itself is adopted to connect the coaxial dual-band horn feed. These two types of feed lines provide a high conversion efficiency of about 98% from TEM or TM01 mode to TE11 mode and a bandwidth of about 10% at each band. The horn feed, with a high power handling capacity, is compact, and a good far-field radiation pattern at each band has been achieved by combining horizontal and vertical corrugations. Thus, the dual-band radiation system has not only realized incoherent power combination, with higher output peak power level, but also is suitable for feeding of, e.g., offset shaped single-reflector antennas in dual-band HPM systems in the future.