To realize the double-mode absorption, the graphene ribbon was embedded into the defective photonic crystal. Based on the rigorous coupled wave method, it is found that the system achieves two perfect absorption modes at 5.1537THz and 5.1970THz, due to the Fabry-Pérot resonance and surface plasmon polariton resonance. At the same time, the impedance of the whole structure was equal to that of the free space. Analysis of key parameters indicate that both modes number and modes-coupling extent can be changed by tuning the chemical potential of graphene electrically. When the chemical potential is 0.7eV, two absorption modes are coupled wholly. Also, the coupling extent can be controlled by adjusting the geometry of graphene ribbon. When the incident light deviates from the normal incidence, the modes number is directly affected by the deflection. This study is helpful to reconstruct the absorption spectrum of terahertz devices.