The plasmons in graphene have the superior properties to metal surface plasmons, such as high field confinement, low Ohmic loss and long wave propagation, highly tunable via electrostatic. More importantly, the frequency of plasmons ranges from terahertz to infrared which indicates that graphene is an ideal candidate for terahertz plamsonics. On the other hand, the strong coupling between incident photons and plasmons in graphene can lead the optical absorption to be enhanced. However, it is difficult for light to couple directly with plasmons in graphene, for the momentum of incident photons cannot match the plasmons in graphene. A metal grating can be used to compensate for the momentum of photons so that it can match that of plasmons in graphene. In this work, we theoretically investigate the effect of plasmons on the terahertz optical absorption of graphene with grating based on finite difference time domain. A great enhancement of electric field component of light field can be obtained near the gold grating strip in the sheet of graphene. Thus, the photons, of which the momentum is compensated for by the grating, can strongly couple with plasmons in graphene. An obviously decrease of the transmission of the graphene structure can be seen at the resonant frequency. The transmission peak corresponds to the resonant frequency spliting into two peaks due to the fact that two plasmon polariton modes are formed by the coupling of photons and palsmons. So we also study the plasmon polariton modes made by coupling photon with palsmon based on the many-body self-consistent method. Two plasmon polariton modes are obtained and an obviously splitting at the resonant frequency can be seen due to the coupling between photons and plasmons. The work conduces to deepening the understanding of the photoelectric properties of graphene and the terahertz plasmonics based on graphene.