Graphene has been considered as a promising material which may find applications in the THz science. In this work, we numerically investigate tunable photonic crystals in the THz range based on stacked graphene/dielelctric layers, a complex pole–residue pair model is used to find the effective permittivity of graphene, which could be easily incorporated into the finite-difference time domain (FDTD) algorithm. Two different schemes of photonic crystal used for extending the bandgap have been simulated through this FDTD technique.Project supported by the Spanish Ministry of Education (Grant No. SB2010-0056), the EU FP7/2007-2013 (Grant No. 205294) (HIRF SE project), the Spanish National Projects (Grant Nos. TEC2010-2084...