The unique properties of graphene have widened its use for antenna applications in the recent years. However, most of previous studies are more focused on using graphene in the Tera Hertz (THz) band due to their favorable surface properties (conductivity or impedance) for antennas. This work investigates the improvement of a graphene-based millimeter wave (mm-wave) microstrip hexagonal patch antenna, its performance is known to be comparable to a conventional copper based version. As expected, the utilizing of non-doped graphene instead of conventional metal, did not has a significant improvement to the antenna performance except for its reflection coefficient in addition to a little reduction in the dielectric loss of antenna. Furthermore, it also leads to increasing in metal losses of antenna structure compared to copper. However, the biasing of the graphene layer is observed to reduce antenna metal losses considerably, besides improving other antenna performance parameters such as radiated power, radiated efficiency and gain.