The band structure of GNM is studied using TB method. It is found that some surface states appear in the vicinity of the Fermi levels. The electron might be trapped on these surface states due to very large effective mass. The increase of the effective bandgap of GNM as the increase of the radius of the nanohole, may be responsible for the increase of current on/off ratio for GNM devices observed in the experiment. Process variations are found to be suppressed effectively in GNM.