In this paper, an efficient lightweight double-layer microwave absorber with impedancematching structure at X-Ku bands was designed, optimized and implemented. First, genetic algorithm (GA) was considered to optimize the thicknesses and material properties for better absorption of the incident electromagnetic wave and reduction of radar cross section (RCS). Next, with the aid of the obtained dielectric and magnetic properties, the microwave absorber was fabricated from magnetodielectric composite materials besides a natural rubber. Finally, the analytical and numerical results were compared with the measurements to check the validity of the design. Experiments showed that the reflection coefficient for each layer backed with a metallic sheet was insufficient; however, for the double layer absorber, the reflectivity measurement values reached up to −28 dB in the case of normal incidence and −17 dB for oblique incidence.