We investigate the photonic bandgaps in graphene-pair arrays. Graphene sheets are installed in a bulk substrate to form periodical graphene photonic crystal. The compound system approves a photonic band structure as a light impinges on it. Multiple stopbands are induced by changing the incident frequency of light. The stopbands widths and their central frequencies could be modulated through the graphene chemical potential. The number of stopbands decreases with the increase in the spatial period of graphene pairs. Otherwise, two full passbands are realized in the parameter space composed of the incident angle and the light frequency. This investigation has potentials applied in tunable multi-stopbands filters.