A dual-polarization frequency-selective rasorber with two absorptive bands at both sides of a passband is presented. Based on the characteristic mode analysis, a circuit analog absorber is designed using a lossy FSS that consists of miniaturized meander lines and lumped resistors. The positions and values of resistors are determined according to the analysis of modal significances and modal current. After that, the presented rasorber is designed by cascading of the lossy FSS and a lossless bandpass FSS. Equivalent circuits of the frequency-selective rasorber are modelled, and surface current distributions of both FSSs are illustrated to explain the operation mechanism. Measurement results show that, under the normal incidence, a minimum insertion loss of 0.27 dB is achieved at a passband around 6 GHz, and the absorption bands with an absorption rate higher than 80% are 2.5 to 4.6 GHz in the lower band and 7.7 to 12 GHz in the higher band, respectively. Our results exhibit good agreements between measurements and simulations.