In this paper, we present an innovative radar absorber composed of a dielectric spacer and a dielectric lossy sheet (DLS), instead of the resistive sheet of the conventional Salisbury screen absorber. We propose carbon nanocomposites as DLS to utilize their structural robustness and advantages in large-area applications, while maintaining a relatively precise thickness. These are laminates made of E-glass fabric/epoxy prepregs containing carbon black (CB), carbon nanotube (CNT), and carbon nanofiber (CNF). The spacer is a pure E-glass fabric/epoxy composite laminate. The optimal design process based on a numerical model of the complex permittivity of the carbon nanocomposites, and a genetic algorithm shows that the real part of the complex permittivity of the sheet is closely related to the reduction of the spacer thickness. In contrast, the variation of the imaginary part is very marginal. The design results show that, in the X-band, the absorber thickness is 3.1 mm for the CB-composites, 2.76 mm for the CNT-composites, and 2.5 mm for the CNF-composites. The 10-dB bandwidth of every absorber is about 3.8 GHz. In the Ku-band, the absorber thickness is 1.95 mm for the CB-composites, 1.85 mm for the CNT-composites, and 1.7 mm for the CNF-composites. The 10-dB bandwidth of every absorber is broader than 5.5 GHz.