We present a wave absorption design consisting of periodical arrays of dielectric bricks on the dielectric substrate, which is coated with single-layered and nonstructured graphene, supported by a thick piece of metal. The design is demonstrated to broadband near-perfect absorption with 0.82 terahertz (THz) bandwidth of over 90% absorption and with central frequency of 1.68 THz. The broadband absorption mechanism originates from two contributions. Firstly, the periodical arrays of dielectric bricks on the nonstructured graphene can provide both a set of graphene plasmon resonances with large relative frequency interval and relative radiation rate γ/ω in the THz range. Secondly, the linewidth of each resonance can be broadened by the far-field interaction between neighboring resonators to overlap and spread over a wide frequency region in the THz range. The design in this paper is simple, and consequently facilitates the fabrication and promotes the application of broadband graphene absorbers.