Thin glass-fiber/epoxy-composite sheets filled with multiwalled carbon nanotubes (MWCNTs) are manufactured to make lightweight honeycomb sandwich microwave absorbers. A multilayered sandwich structure of thin nanocomposite sheets and honeycomb spacers have been also proposed and developed to work in a wide frequency range. The nanocomposite sheets are prepared from 0.5, 1.0, 1.5, 2.0, and 2.5 wt. % of MWCNTs. A commercially available simulation software computer simulation technology (CST) microwave studio was used for the designing and development of radar absorbing structure (RAS) composed of MWCNTs/glass-fiber/epoxy-composite sheets and honeycomb cores. The measurements of return loss (RL) from sandwich structures with 5 mm and 20 mm honeycomb cores in the Ku band (11–17 GHz) show that maximum RL is achieved at 11 GHz and 16 GHz, respectively. The stacking of three nanocomposite sheets and three 5 mm-thick honeycomb spacers produced a wide band microwave absorber with −10 dB RL over 9 GHz bandwidth.