Density functional theory was used to study the effects of different types of oxygen-containing functional groups on the adsorption of oxygen molecules and single active oxygen atoms on carbonaceous materials. During gasification or combustion reactions of carbonaceous materials, oxygen-containing functional groups such as hydroxyl(-OH), carbonyl(-CO), quinone(-O), and carboxyl(-COOH) are often present on the edge of graphite and can affect graphite's chemical properties. When oxygen-containing functional groups appear on a graphite surface, the oxygen molecules are strongly adsorbed onto the surface to form a four-member ring structure. At the same time, the O-O bond is greatly weakened and easily broken. The adsorption energy value indicates that the adsorption of oxygen molecules changes from physisorption to chemisorption for oxygen-containing functional groups on the edge of a graphite surface. In addition, our results indicate that the adsorption energy depends on the type of oxygen-containing functional group. When a single active oxygen atom is adsorbed on the bridge site of graphite, it gives rise to a stable epoxy structure. Epoxy can cause deformation of the graphite lattice due to the transition of graphite from sp2 to sp3 after the addition of an oxygen atom. For quinone group on the edge of graphite, oxygen atoms react with carbon atoms to form the precursor of CO2. Similarly, the single active oxygen atoms of carbonyl groups can interact with edge carbon atoms to form the precursor of CO2. The results show that oxygen-containing functional groups on graphite surfaces enhance the activity of graphite, which promotes adsorption on the graphite surface.