A terahertz absorber composed of three-layer micro-structure gratings was designed based on the effective medium theory and the theory of multi-layer antireflection coating. The absorber was designed on the heavily boron doped silicon. By using the finite-difference time-domain method, the influence of the grating period, width and depth on the reflection coefficient was analyzed. The numerical simulation results show that, in the range of 0~3 THz, more than 98% terahertz absorption can be achieved with a bandwidth of 1.3 THz and over 95% terahertz absorption can be obtained with a bandwidth of 2.1 THz. The high performance of the absorber was explained by the rigorous coupled-wave theory, which suggests that the interaction among the different grating diffraction modes reduces the reflection of the incident wave and increases the absorption rate of the absorber. By structural parameter optimization, the absorber can achieve more than 95% broadband terahertz absorption in the range of 0.6~6 THz. The absorber may be a valuable candidate for use in Terahertz imaging and detecting.