In this paper, the physical adsorption of volatile organic compounds (VOCs) such as methyl chloride (CH3Cl), carbon disulfide (CS2), dimethyl sulfide (C2H6S), and benzene (C6H6) by three models of activated carbon (without a functional group, with a pyridine-containing functional group, and with a pyrrole-containing functional group) was simulated. The surface electrostatic potential (ESP), physical adsorption energy, and non-covalent interaction between activated carbon and VOC molecules were analyzed based on the density functional theory (DFT). The effect mechanism of nitrogen-containing functional groups on VOC adsorption by activated carbon was determined. Our simulations showed that nitrogen-containing functional groups can change the surface ESP and polarity of activated carbon. The pyrrole functional group is conducive to CH3Cl and CS2 adsorption on the activated carbon plane, while the pyridine functional group is relatively small or even unfavorable for CH3Cl and CS2 adsorption on the activated carbon plane. The promotional effect of the pyrrole functional group on the adsorption of C2H6S is more significant than that of the pyridine functional group. The adsorption of C6H6 on activated carbon occurs through parallel-displaced π–π stacking interactions, in which functional groups have little influence on it. The adsorption energy of VOCs on the activated carbon plane is higher than that at the edge, so VOCs are more likely to be adsorbed on the activated carbon plane.