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To understand the effect of Au doping on graphene nanoribbons, Au doped armchair graphene nanoribbons (AGNRs) are investigated using the first principles calculations.The energy band structure the total density of states and project density of states of Au doped AGNRs are calculated to compare with bare, H terminated AGNRs.The Fermi level islocated on the valence band so that the AGNRs of doping Au become into degenerate semiconductor.The Au doping AGNRs are an indirect band gap semiconductor.The hybridization between C-2p and Au-6p electronic states are strongly in the conduction band.The project density of states is calculated which reveals the localization and hybridization between C-2p and Au-6s, 5d electronic states are much stronger in the valence band.