The relatively high sheet resistance of graphene compared with indium tin oxide (ITO) blocks the applications of graphene as transparent electrodes in organic light-emitting diodes. A novel copper (Cu)/graphene composite electrode is presented and employed as the anode of a top-emission organic light-emitting diode with the structure of Cu/graphene/V2O5/NPB/Alq3/Alq3: C545T/Bphen: Cs2CO3/Sm/Au. The Cu/graphene composite electrodes are fabricated by growing graphene directly on Cu substrates via the chemical vapor deposition method without any transfer process. The maxima of current efficiency and power efficiency of a typical Cu/graphene composite anode device reach 6.1 cd/A and 7.6 lm/W, respectively, which are markedly higher than those of the control devices with a graphene anode, a Cu anode or an ITO anode. The low sheet resistance of the composite electrode, the high quality of graphene without any transfer process and the avoidance of wave guiding loss in glass or polyethylene terephthalate substrates result in the improvements of light emission efficiencies.