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In this paper, one-dimensional (1D) and two-dimensional (2D) graphene-based plasmonic photonic crystals (PhCs) are proposed. The band structures and density of states (DOS) have been numerically investigated. Photonic band gaps (PBGs) are found in both 1D and 2D PhCs. Meanwhile, graphene-based plasmonic PhC nanocavity with resonant frequency around 175 THz, is realized by introducing point defect, where the chemical potential is from 0.085 to 0.25 eV, in a 2D PhC. Also, the bending wvaguide and the beam splitter are realized by introducing the line defect into the 2D PhC.