The adsorption of the hydrogen peroxide (H2O2) molecule, which is known as the common form of reactive oxygen species in living cells, was investigated theoretically over pure graphene and heteroatom- (nitrogen-, boron-, and sulfur-) and metal-atom- (silver-, gold-, copper-, palladium-, and platinum-) doped graphene surfaces using the density functional theory (DFT) method. This study involved the optimization of pure and doped graphene surfaces, adsorption of the gas molecule on top of the doped atoms and neighboring carbon atoms, and analysis of the behavior of the gas molecule over the various adsorption sites. First principles calculations revealed that the copper-doped and silver-doped graphene surfaces are the most thermodynamically favorable surfaces for the direct formation of water molecules. Moreover, the sulfur-doped surface exhibits a superior performance among the heteroatom-doped surfaces. Additionally, the gap between the orbital energies of the system was found to have an effect on the surface behavior of the H2O2 molecule.