Molten salt is used as primary coolant flowing through graphite moderator channel of a molten salt reactor. Working at high temperature under radiation environment, the pore network structure of nuclear graphite should be well understood. In this paper, X-ray tomography is employed to study the 3D pore structure characteristics of nuclear grades graphite of IG-110, NBG-18 and NG-CT-10, and permeability simulation through geometries are performed. The porosity, number of pores and throats, coordination number and pore surface are obtained. NG-CT-10 is of similar microstructure to IG-110, but differs significantly from NBG-18. The absolute permeabilities of IG-110, NG-CT-10 and NBG-18 are 0.064, 0.090 and 0.106 mD, respectively. This study provides basis for future research on graphite infiltration experiment.