Single-layer metallic rings are the effective structure cell which are widely used to design single-band and multiband perfect metamaterial absorbers owning to their electromagnetic resonance. However, the absorbers based on the single-layer metallic rings have a common shortcoming, that is the narrow absorption bandwidth. To overcome the limitations, here we proposed a single-layer, flexible and broadband terahertz metamaterial absorber, which consists of four sub-cells with multiple metal rings and a metal ground plane separated by a dielectric layer. By enhancing the coupling response between adjacent metallic rings and merging the adjacent resonant peaks of multi-resonators, we experimentally observed broadband characteristics at the terahertz band. The average absorption of 88% from 0.63 to 1.34 THz and the relative absorption bandwidth of 95% at the incident angle of 15o for TE polarization. Correspondingly, for TM polarization the absorption of more than 80% from 0.61 to 1.1 THz with the relative absorption bandwidth of 80% were also observed. The results went far beyond the previous single-layer absorbers based on metal rings and were much better than the fractal-cross structure reported recently [Kenney et al., ACS Photonics 4, 2604 (2017)]. We had reason to believe that the presented terahertz metamaterial absorber with broad absorption bandwidth and simple structure can find important applications in communication, stealth, energy harvesting systems and so on.