A broadband terahertz metamaterial absorber is proposed based on the double composite structure layers (CSLs). The composite structure layer I and composite structure layer II comprise four different-sized gold rings and square plates, respectively. Further, the finite difference time domain (FDTD) method is employed to theoretically investigate and discuss the effects of absorption spectrum, magnetic field distribution, surface current distribution, polarization angle, and incident angle on absorption. The results show that the high-order resonance peaks can be effectively suppressed by this absorber. Furthermore, in case of normal incidence, the absorption bandwidth corresponding to absorptivity greater than 90% is 0.722 THz, and its central frequency is approximately 2.041 THz.