Abstract: A theoretical research on terahertz electromagnetic characteristics of one-dimensional graphene-photonic crystal is carried out by using the finite-difference time-domain (FDTD) with a surface boundary condition in this paper. Firstly, the reflection and transmission coefficient are given by the FDTD at both sides of the graphene in the terahertz spectrum. Comparison of the simulated results with the analytic ones proved the correctness of the simulation method. Then the absorption characteristics of one-dimensional graphene photonic crystal are studied in the terahertz range. Results with different models of photonic crystal indicate that the localization casued by surface defect can greatly enhance the absorption of graphene which is located in the surface of photonic crystal.