The adsorption of six free radicals (FRs) respectively on a graphene fragment was studied using a density functional tight-binding method with the inclusion of an empirical dispersion term in total energy. The results indicate that the different interaction paths between the FRs and the graphene lead to different forms of physical (PA) or chemical adsorptions (CA). The CA appears only in the condition where some of the nonhydrogen atoms are closer to the graphene, with the deformation occurring in the latter. The charge transfer increases with the increase in adsorption energy in every FR-graphene system. Although the deformation in the graphene is negligible in all PA cases, the FR is closer to the graphene and the graphene deformation is clearer in all CA cases, with all atomic displacements being larger than 0.1 Å. Our findings are useful not only for FR scavenging but also for studying the interaction between general molecules and material surfaces.