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We design an ultra-thin multi-band polarization-insensitive metamaterial absorber (MMA) using a single circular sector resonator (CSR) structure in the microwave region. Simulated results show that the proposed MMA has three distinctive absorption peaks at 3.35 GHz, 8.65 GHz, and 12.44 GHz, with absorbance of 98.8%, 99.7%, and 98.3%, respectively, which agree well with an experiment. Simulated surface current distributions of the unit-cell structure reveal that the triple-band absorption mainly originates from multiple-harmonic magnetic resonance. The proposed triple-band MMA can remain at a high absorption level for all polarization of both transverse-electric (TE) and transverse-magnetic (TM) modes under normal incidence. Moreover, by further optimizing the geometric parameters of the CSRs, four-band and five-band MMAs can also be obtained. Thus, our design will have potential application in detection, sensing, and stealth technology.