In this paper, a multi-band metasurface absorber is designed, measured and investigated. There are four centrosymmetric two-tangent copper trapezoids that make up its unit cell. The parameters of the unit cell have great influence on the frequency of absorption peaks, with optimized parameters leading to absorptivity of 99.4%, 93.9% and 99.7% at 4.80GHz, 8.68GHz and 10.92GHz, respectively. The physical mechanism of absorption is further analyzed based on the distributions of surface current, electric and magnetic field, as well as the impedance matching. Furthermore, the absorber exhibits characteristics of polarization insensitivity and incident sensitivity, which are demonstrated through experiment. In addition, the proposed absorber is able to monitor different environments that the sensitivities are 0.15GHz/PIU, 0.50GHz/PIU and 1.53GHz/PIU at three absorption peaks. In addition, the FOM of the proposed sensors at corresponding resonant frequencies are 0.68, 1.61 and 4.78, respectively. The result reflects that the proposed metasurface shows effective sensing abilities. The designed metasurface absorber has potential applications in both military and civil fields.