Flexible and lightweight conducting polymer composites for application as electromagnetic wave absorbing (EMWA) materials were prepared by a one-step melt-blending procedure using a polypropylene/EVA (50:50 wt%) blend filled with carbon nanotube. The co-continuous structure and the preferential localization of CNT in the EVA phase and at the interface are responsible for the low percolation threshold (0.02 vol%) and a conductivity of 10−3 S m−1 with 1.5 wt% of CNT. Metal-backed configuration was used for measuring the electromagnetic attenuation in both X- (8–12 GHz) and Ku-band (12–18 GHz). Samples 3 mm thick were compared with three-layered structures constituted by three layers of 1 mm each. The best EMWA response in terms of minimum reflection loss (RL) (−35.5 dB) and large effective absorption bandwidth (EAB) (6.6 GHz) was observed for the three-layered system with the appropriate arrangement. The low cost of polymer components and processing conditions, lightweight, and processability, due to the low amount of CNT, make this system a promising candidate for applications in both civilian and military areas as telecommunication and stealth technology.