A method of fabricating a graphene electronic device includes (a) forming a first electrode and a second electrode spaced apart from each other, on a substrate; (b) forming supporting patterns on the first electrode and the second electrode; (c) coating the supporting patterns with graphene-oxide-containing solution to form composite patterns; and (d) separating the supporting patterns from the composite patterns. The step of forming supporting patterns may expose end portions of the first and second electrodes and the substrate between the end portions and be accomplished by providing a mask on the first and second electrodes; and electrospinning a polymer solution on the first and second electrodes with the mask. The supporting patterns may be composed of polymer fibers.