A novel absorbing material with a flexible sandwich structure (S121) was designed and assembled using light-weight foams of Polydimethylsiloxane (PDMS) to achieve a full X-band absorption. The PDMS foams based on the composites of hollow polyaniline and MWCNTs (HPC) were prepared by means of impregnation technology selecting sugar cubes as a template. For the construction of sandwich S121, the upper and lower layers were HPC-PDMS foams (dfoam = 1.0 mm) and the middle layer was HPC-PDMS film (dfilm = 0.5 mm). The SEM results revealed plentiful pores existed in S121, which would endow S121 with the traits of light-weight and lower density. The absorption performance of S121, single-layer HPC-PDMS foam (S1) and single-layer HPC-PDMS film (S2) had been characterized. Of importance, S121 achieved full absorption in X-band and its minimum reflection loss (RLmin) reached −32.65 dB at 9.5 GHz. In contrast, the RLmin of S1 and S2 were only −15.42 dB and −11.72 dB. The frequency regions with RL < −10 dB of S1 and S2 were surprisingly narrow, which were 1.5 GHz and 0.4 GHz, respectively. The results indicated that the design of S121 demonstrated a synergistic effect of foams and film, which was helpful to enhance absorption and realize an X-band full absorption. Of great significance, due to the excellent flexibility of S121, after bending and compressing many times, RLmin value is nearly identical to that of original S121, and the effective bandwidth is also full coverage of X-band. The results showed that the proposed S121 design is feasible for applications in X-band.