In this paper, we have shown that perfect absorption at terahertz frequencies can be achieved by using a composite structure where graphene is coated on one-dimensional photonic crystal (1DPC) separated by a dielectric. Due to the excitation of optical Tamm states (OTSs) at the interface between the graphene and 1DPC, a strong absorption phenomenon occurs induced by the coupling of the incident light and OTSs. Although the perfect absorption produced by a metal–distributed Bragg reflector structure has been researched extensively, it is generally at a fixed frequency and not tunable. Here, we show that the perfect absorption at terahertz frequency not only can be tuned to different frequencies but also exhibits a high absorption over a wide angle range. In addition, the absorption of the proposed structure is insensitive to the polarization, and multichannel absorption can be realized by controlling the thickness of the top layer.