This paper presents the design and the realization process for radar absorbing panels made of composite materials. It is demonstrated that the proper selection of the carbon fiber length and volume fraction allows reducing sensibly the overall thickness of the screen compared to a standard absorber, and obtaining at the same time broad-band absorption response in the X- and Ku-bands. To this end, the carbon fiber composite material realizing the lossy sheet of the absorbing screen is designed by simulation in order to have tailored complex effective permittivity. Two prototypes of absorbing screens are realized and tested experimentally. The first one is a three-layer panel, characterized by reflection coefficient lower than -10 dB in the frequency range from 8 to 14 GHz, and total thickness of 4.5 mm. The second one is a five-layer panel with reflection coefficient less than -20 dB in the range 9-18 GHz, and total thickness of 5.5 mm.