This article presents data on the synthesis, identification, computer simulation and biocompatibility of graphene oxide (GO) functionalized with L-cysteine (GFC). It was determined that GO reacts with L-cysteine in two different ways: in an alkaline medium, L-cysteine reduces functional groups on the surface and at the boundaries of GO; with heating and the use of thionyl chloride, L-cysteine covalently attaches to GO through carboxylic groups only at the boundaries. The identification of GO, reduced graphene oxide and GFC was performed using various physicochemical methods, including infrared spectroscopy, Raman spectroscopy, X-ray diffraction, X-ray photoelectron spectroscopy, thermogravimetric analysis, scanning electron microscopy and high-resolution transmission electron microscopy. Biocompatibility experiments included erythrocyte hemolysis, platelet aggregation, photodynamic and antiradical activity, binding to human serum albumin, and geno- and cytotoxicity studies. Applying density functional theory and molecular dynamics allowed us to obtain the structural and dynamic characteristics of a GFC–water binary system.