A terahertz metasurface perfect absorber with multi-band performance is demonstrated. The absorber is composed of a ground plane and four split-ring resonators (SRRs) with different dimensions, separated by a dielectric spacer. The numerical simulation results illustrate that the proposed absorber has four distinct absorption peaks at resonance frequencies of 4.24, 5.66, 7.22, and 8.97 THz, with absorption rates of 96.8%, 99.3%, 97.3%, and 99.9%, respectively. Moreover, the corresponding full width at half-maximum (FWHM) values are about 0.27, 0.35, 0.32, and 0.42 THz, respectively, which are much broader than those of previously reported absorbers. Besides, the calculated magnetic field distributions allow us to understand the absorption mechanism in detail. The effects of incident angle and azimuthal angle on the absorber are also investigated. The results show that the proposed absorber is partially sensitive to the incident angle, which makes this design promising for practical applications in terahertz imagers and detectors.