A novel method was investigated to achieve in-plane graphene surface plasmon anderson localization in mid-infrared region by transferring a graphene sheet on the one-dimensional random silicon gratings. By adjusting the Fermi level of graphene, the resonance wavelengths of anderson localizated graphene surface plasmon caused by its random nature can be easily tuned. The field intenstiy of localizated graphene surface plasmon is higher than the corresponding one in the periodic silicon gratings 70 times when the Fermi level is set to be 0.6 eV. The structure proposed can be appiled to the tunable integrated filters, broadband modulators and plasmonic sensors.