As a new engineering dielectric, vegetable insulating oil is widely used in electrical equipment. Small polar molecules such as alcohol and acid will be produced during the oil-immersed electrical equipment operation, which seriously affects the safety of equipment. The polar molecule can be removed by using functional fossil graphene materials. However, the structural design and group modification of graphene materials lack a theoretical basis. Therefore, in this paper, molecular dynamics (MD) and quantum mechanics theory (Dmol3) were utilized to study the adsorption kinetics and mechanism of graphene (GE), porous graphene (PGE), porous hydroxy graphene (HPGE), and porous graphene modified by hydroxyl and carboxyl groups (COOH-HPGE) on polar small molecules in vegetable oil. The results show that graphene-based materials can effectively adsorb polar small molecules in vegetable oil, and that the modification of graphene materials with carboxyl and hydroxyl groups improves their adsorption ability for polar small molecules, which is attributed to the conversion of physical adsorption to chemical adsorption by the modification of oxygen-containing groups. This study provides a theoretical basis for the design and preparation of graphene materials with high adsorption properties.