A novel cationic polymer, poly[2-(tert-butylaminoethyl) methacrylate] (PTA), effectively kills various strains of bacteria with low toxicity to tissue cells. Graphene-based materials demonstrate exceptional electron transport capability, antibacterial activity, favorable nontoxicity, and versatile applicability. PTA can be grafted onto the graphene oxide (GO) surface (GO-g-PTA) to enhance the antimicrobial efficiency of the latter against Staphylococcus aureus (S. aureus). In this study, GO-g-PTA powders were successfully synthesized via free radical polymerization (GO-g-PTA-F) and atom transfer radical polymerization (GO-g-PTA-A). The antimicrobial efficiencies of graphene nanosheets (GNSs), GO-g-PTA-F, and GO-g-PTA-A were then investigated. Addition of GNS, GO-g-PTA-F, and GO-g-PTA-A to the PVA nanofibers was carried out elucidate the effects of filler amount and physical treatment on the morphology, microstructure, crystallization behaviors, antimicrobial efficiency, and cytotoxicity of the composite fibers. Finally, the potential applications of electrospun PVA/GNS, PVA/GO-g-PTA-F, and PVA/GO-g-PTA-A composite nanofiber mats to chronic wound care were evaluated. The resulting PVA/GO-g-PTA-A composite nanofiber mats showed enhanced antimicrobial ability against S. aureus compared with the PVA/GNS and PVA/GO-g-PTA-F composite nanofiber mats at the same filler volume percentage.