SO2 (sulfur dioxide) is a toxic substance emitted into the environment due to burning sulfur-containing fossil fuels in cars, factories, power plants, and homes. This issue is of grave concern because of its negative effects on the environment and human health. Therefore, the search for a material capable of interacting to detect SO2 and the research on developing effective materials for gas detection holds significant importance in the realm of environmental and health applications. It is well known that one of the effective methods for predicting the structure and electronic properties of systems capable of interacting with a molecule is a method based on quantum mechanical approaches. In this work, the DFT (Density Functional Theory) program DMol3 in Materials Studio was used to study the interactions between the SO2 molecule and four systems. The adsorption energy, bond lengths, bond angle, charge transfer, and density of states of SO2 molecule on pristine graphene, N-doped graphene, Ga-doped graphene, and -Ga-N- co-doped graphene were investigated using DFT calculations. The obtained data indicate that the bonding between the SO2 molecule and pristine graphene is relatively weak, with a binding energy of −0.32 eV and a bond length of 3.06 Å, indicating physical adsorption. Next, the adsorption of the molecule on an N-doped graphene system was considered. The adsorption of SO2 molecules on N-doped graphene is negligible; generally, the interaction of SO2 molecules with this system does not significantly change the electronic properties. However, the adsorption energy of the gas molecule on Ga-doped graphene relative to pristine graphene increased significantly. The evidence of chemisorption is increased adsorption energy and decreased adsorption distance between SO2 and Ga-doped graphene. In addition, our results show that introducing -Ga-N- co-dopants of an “ortho” configuration into pristine graphene significantly affects the adsorption between the gas molecule and graphene. Thus, this approach is significantly practical in the adsorption of SO2 molecules.