We presented and manufactured a triple-band terahertz (THz) metamaterial absorber with three concentric square ring metallic resonators, a polyethylene terephthalate (PET) layer, and a metallic substrate. The simulation results demonstrate that the absorptivity of 99.5%, 86.4%, and 98.4% can be achieved at resonant frequency of 0.337, 0.496, and 0.718 THz, respectively. The experimental results show three distinct absorption peaks at 0.366, 0.512, and 0.751 THz, which is mostly agreement with the simulation. We analyzed the absorption mechanism from the distribution of electric and magnetic fields. The sensitivity of the three peaks of this triple-band absorber to the surrounding is 72, 103.5, 139.5 GHz/RIU, respectively. In addition, the absorber is polarization insensitive because of the symmetric configuration. The absorber can simultaneously exhibit high absorption effect at incident angles up to 60° for transverse electric (TE) polarization and 70° for transverse magnetic (TM) polarization. This presented terahertz metamaterial absorber with a triple-band absorption and easy fabrication can find important applications in biological sensing, THz imaging, filter and optical communication.