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A new design of a metallic dual-band electromagnetic band-gap (EBG) suitable to feed a reflector antenna for space multibeam applications is introduced in this letter. The EBG antenna is composed of double-layer frequency selective surfaces (FSS) arranged in the longitudinal direction and a square horn as a feed. First, we devise a technique to adapt the dual-band EBG antenna characteristics for this space application, which requires the same EBG phase center and the same radiation patterns for both frequency bands. Then, a dual-band EBG antenna has been designed. Finally, a prototype is realized, and the experimental measurements are compared with success to the simulated ones. The same phase center has been obtained at 5 and 7.5 GHz. This antenna is suitable to feed a reflector antenna with a focal-length-to-diameter (F/D) ratio of 1.2. The performances of the offset reflector fed by this antenna are good with a maximum efficiency about 77% and with sidelobes levels always better than -22 dB for both frequency bands.