A composite lattice two-dimensional graphene plasmon polariton crystal structure is proposed, which composed of periodically arranged primitive cells with four graphene nanodisks. The energy-band structure and density of states of graphene plasmon polariton crystals are obtained by iteratively solving the eigenfrequencies with the finite element method. The numerical simulation results show that, in the proposed structure, there exists a complete photonic bandgap with a bandgap width of 5.7 THz, and the position and width of this bandgap can be tuned by modifying the chemical potential of graphene. The proposed structure can be applied in the techniques such as high density surface plasmon polariton integrated circuit and on-chip plasmon polariton interconnection.