In this paper, a three-layer composite absorber with a split-spiral frequency selective surface layer clamped by two traditional absorber layers, is designed. The 1.4, 1.7 and 2.0 mm thick composites reach, respectively, the bandwidth values of 9.29, 6.69 and 7.11 GHz at a reflectivity lower than the -10 dB level, whose operating bandwidths are increased by 159.5%, 69.3% and 129.4% compared with those of the traditional absorbing sheet without frequency selective surface (under otherwise identical parameters). Further, the paper shows that the thinner composite sheet can have more excellent performance in reflection than the absorb sheets. The split-spiral frequency selective surfaces generated multiple resonance can be used to generate additional absorption band. The simulation results show that the embedded frequency selective surface improves an impedance matching between absorber with the free space, which changes the reflection of the absorbing sheet.