Arrangements of hydroxyl groups on graphene sheets were systematically investigated using density functional theory calculations that included van der Waals interactions. Results show that hydroxyl groups tend to gather at para-positions on graphene sheets to generate perfect ring-like hexahydroxyl group adsorption. The close proximity of hydroxyl groups is in good agreement with the experimental separation between unoxidized, aromatic and oxidized, saturated regions in graphene oxide. The orientation of hydrogen atoms in hydroxyl groups creates both O–H···O and O–H···π hydrogen bonds. Calculations also indicated that the binding energy per hydroxyl group follows a logarithmic function with respect to the number of hydroxyl groups. Besides, the opening band gap was observed for several derivatives, and the relationship between the band gap and O/C ratio was found to be nonmonotonic. Analysis of the density of states showed that bands around the Fermi levels of derivatives between graphene and hydroxyl groups are mainly composed of 2p z orbitals of carbon and oxygen atoms.