The design of multi-band metamaterial perfect absorbers is of great significance in the field of multi-color optics. In this study, a multi-band metal-insulator-metal metamaterial absorber is designed. Its surface electromagnetic response unit is a three-loop nested metal ring array. The finite-difference time-domain method is used to calculate the absorption spectra and electromagnetic field density distributions of the unit. The results show three absorption peaks at 1.44, 2.28, and 3.25 μm with maximal absorptivity of 98.5%, 99.6%, and 99.9%, respectively. The physical mechanism for these peaks is ascribed to the excitation of magnetic polaritons. The influence of the structural geometric parameters on the resonance is systematically analyzed. By altering the height and outer diameter of metal rings, different resonance wavelengths can be independently tuned. The absorption spectra of the structure are very robust to the polarization angle of incident light. In addition, the refractive index infrared sensing performance of the metamaterial absorber is examined. It is found that the structure exhibits excellent performance for refractive index sensing. The maximum figure of merit can reach 8.3 RIU -1(RIU is the refractivity unit), and the corresponding sensitivity reaches 1.08 μm·RIU -1. The proposed absorber can be applied to the sensing field and provide new insights for the design of other metamaterials.