The possibility of creating antennas of the 5G standard (5.2–5.9 GHz) with specified electrodynamic characteristics by printing layers of variable thickness using a graphene suspension has been substantiated experimentally and by computer simulation. A graphene suspension for screen printing on photographic paper and other flexible substrates was prepared by means of exfoliation from graphite. The relation between the graphene layer thickness and its sheet resistance was studied with the aim of determining the required thickness of the antenna conductive layer. To create a two-sided dipole, a technology has been developed for the double-sided deposition of graphene layers on photographic paper. The electrodynamic characteristics of graphene and copper antennas of identical design are compared. The antenna design corresponds to the operating frequency of 2.4 GHz. It was found that the use of graphene as a conductive layer made it possible to suppress the fundamental (first) harmonic (2.45 GHz) and to observe radiation at the second harmonic (5.75 GHz). This effect is assumed to observe in the case when the thickness of graphene is lower than that of the skin depth. The result indicates the possibility of changing the antenna electrodynamic characteristics by adjusting the graphene layer thickness.