In this work, we have manually constructed several single-walled carbon nanotube supported single metal atom (Al, Zn, Fe) catalysts (Al-SWCNTs, Zn-SWCNTs, Fe-SWCNTs) and employed them to catalyse the synthesis of hydrogen peroxide with the aid of density functional theory calculations, in which several water and oxygen molecules are included as reactants. Specifically, three different possible reaction pathways are studied in detail and relevant reactants, transition states, and products are optimized. Their activation energies are compared with each other, based on which the optimal reaction path is selected and the possible side products are also discussed. In addition, we have also calculated the relevant electron densities and densities of states of these three catalysts to help reveal the different effects after introducing different metal atoms. These physical properties are possibly related to their catalytic performances. Our results are not only consistent with previous experiments investigating the catalyzing reaction using Zn-SWCNTs, but also predict the catalytic properties of Al-SWCNTs and Fe-SWCNTs in comparison with Zn-SWCNTs.