Graphene is widely used in tunable photonic devices due to its numerous exotic and exceptional properties that are not found in conventional materials, such as high electron mobility, ultra-thin width, ease of integration and good tunability. In this paper, we propose a terahertz metamaterial absorber that is based on patterned graphene, which consists of stacked graphene disk layers, open ring graphene pattern layers and metal bottom layers, all separated by insulating dielectric layers. Simulation results showed that the designed absorber achieved almost perfect broadband absorption at 0.53–1.50 THz and exhibited polarization-insensitive and angle-insensitive characteristics. In addition, the absorption characteristics of the absorber can be adjusted by changing the Fermi energy of graphene and the geometrical parameters of the structure. The above results indicate that the designed absorber can be applied to photodetectors, photosensors and optoelectronic devices.