A three-band tunable polarization-insensitive metamaterial absorber is proposed in this paper. The unit cell of the absorber is composed of a dielectric substrate, a metal patch, and four varactor diodes welded on the top layer. A simple metal via bias network is designed to facilitate the absorption frequency tuning of the absorber. The simulation results show that when there is no bias voltage (0 V), the proposed absorber has three absorption peaks of 88%, 99.5%, and 99.8% under normal incidence at 7.27, 10.93, and 15.84 GHz, respectively. Furthermore, by adjusting the reverse bias voltage (0-19 V) of the varactor, the first absorption peak of the absorber can be tuned from 7.27 to 8.2 GHz and the second absorption peak tuned from 10.93 to 11.4 GHz.Meanwhile, the tuning range for the third absorption peak is 15.84-16.1 GHz. Furthermore, the three-band absorption and frequency tunable characteristics of the absorber are confirmed by experimental tests.