A terahertz absorber is designed by integrating the graphene dielectric stack (GDS) above and the metal grating below. The GDS is formed through arranging the graphene monolayer and dielectric film periodically. In the case of impedance matching, two near-unity absorption modes arise as the coupling result of Fabry-Perot (FP) resonance and surface plasmon polaritons (SPP) resonance. Tuning the chemical potential or the period of GDS, both modes can be shifted. Changing the period or the duty cycle of metal grating, all of the locations and amplitudes of modes along with the peak-peak distance between modes are controllable. Altering the thickness of dielectric slab, these modes move towards the same direction linearly almost. Deviating the normal incidence, the number of absorption modes can be increased. The designed graphene absorber should be useful to multiple targets sensing, photoelectric detection and frequency conversion of nonlinear system.