This paper reports on a numerical study of the six-band metamaterial absorber composed of two alternating stack of metallic-dielectric layers on top of a continuous metallic plane. Six obvious resonance peaks with high absorption performance (average larger than 99.37%) are realized. The first, third, fifth, and the second, fourth, sixth resonance absorption bands are attributed to the multiple-order responses (i.e., the 1-, 3- and 5-order responses) of the bottom- and top-layer of the structure, respectively, and thus the absorption mechanism of six-band absorber is due to the combination of two sets of the multiple-order resonances of these two layers. Besides, the size changes of the metallic layers have the ability to tune the frequencies of the six-band absorber. Employing the results, we also present a six-band polarization tunable absorber through varying the sizes of the structure in two orthogonal polarization directions. Moreover, nine-band terahertz absorber can be achieved by using a three-layer stacked structure. Simulation results indicate that the absorber possesses nine distinct resonance bands, and average absorptivities of them are larger than 94.03%. The six-band or nine-band absorbers obtained here have potential applications in many optoelectronic and engineering technology areas.