The absorption enhancement in the graphene monolayer for the terahertz frequency is investigated. This is achieved by placing the graphene monolayer on a dielectric grating backed with a reduced Bragg grating and a metallic mirror. Complete absorption is achieved at resonance and the absorption spectra exhibit an ultranarrow shape, which is attributed to the combined effects of the guided mode resonance with dielectric grating and the photonic bandgap with Bragg grating. Moreover, the designed graphene absorber possesses antenna-like response and thus can be used as a thermal emitter with high directionality. To disclose the physical origins of such absorption effects, the electric-field intensity distributions are investigated. Furthermore, the peak position of the absorption spectra can be tuned by only a change in the Fermi level. Our results may potentially be used for developing the next-generation graphene-based optoelectronic devices.