In this study, carbon nanotube papers were employed in fabricating thin and broadband radar absorbing structures (RAS). Different concentrations of the CNT papers have been made by using a vacuum filtration method, with 20 × 20 cm in size and 21‐27 μm in thickness. An epoxy resin was added into the CNT paper and then cured to become a composite with 1‐5 wt.% of CNTs and 83‐309 μm in thickness. The complex permittivity and permeability (ε′, ε″, μ′, μ″) of the CNT paper composites were measured using the transmission/reflection method in the frequency range of 2‐18 GHz. The results reveal that the real (ε′) and imaginary (ε″) parts of the complex permittivity are increased with the CNT concentration. The ε′ of 5 wt.% CNT sample reaches 323 at 2 GHz and then decreases to 49.0 at 18 GHz. The ε″ reaches 321 at 2 GHz and decreases to 26.0 at 18 GHz. The CNT paper composite combined with a glass fabric composite used for a dielectric spacer is fabricated for an innovative RAS and the reflection loss is measured using the arch method in a microwave anechoic chamber. The results show that the 5 wt.% CNT paper composite/glass fabric composite absorbers attain maximum reflection loss of −13.3 dB at 12.0 GHz, −13.8 dB  at 10.0 GHz, and −16.0 dB at 7.5 GHz for spacer thickness of 1.5, 2.0, and 3.0 mm, respectively.