The optical Tamm state (OTS), which exists generally at the interface between metal and a dielectric Bragg mirror, has been studied extensively in the visible and near infrared spectra. Nevertheless, OTS in the terahertz (THz) region normally receives far less attention. In this Letter, we demonstrate the physical mechanism of OTS at the interface between graphene and a dielectric Bragg mirror in the THz frequency band by applying the transfer matrix method and dispersion characteristics. Based on such mechanisms, we propose an efficient method that can precisely generate and control OTS at a desired angle and frequency. Moreover, we show that the OTS is dependent on the optical conductivity of graphene, making the graphene–dielectric-Bragg-mirror a good candidate for dynamic tunable OTS device in the THz frequency range.