To achieve the broad utilization of the full functionality of graphene (GR) in devices, a transfer method should be developed that can simplify the process without leaving residue of the insulating supporting layer on the surface of GR. Furthermore, stable GR doping without the use of an insulating polymer is required. Here, a new GR transfer method that uses a popular conducting polymer, poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS), is reported as a new supporting layer for the transfer of GR films that are synthesized by chemical vapor deposition. The GR/PEDOT:PSS bilayer can be directly utilized without the removal process. Therefore, this transfer method simplifies the transfer process and solves the residue problem of conventional transfer methods. The stable doping of GR films is simultaneously achieved by using the PEDOT:PSS layer. The new GR/PEDOT:PSS hybrid electrodes are fully functional in polymer solar cells and polymer light-emitting diodes, outperforming the conventionally transferred GR electrodes and indium tin oxide electrodes.