Graphene can be used as a drug carrier of doxorubicin (DOX) to reduce the side effects of doxorubicin. However, there is limited research on the surface chemical modifications and biological effects of graphene oxide (GO). Therefore, it is necessary to explore the DOX affinity of different oxygen-containing functional groups in the graphene system. We constructed graphene system models and studied the structure and distribution of epoxy and hydroxyl groups on the carbon surface. Based on molecular dynamics simulations and density functional theory (DFT), we investigated the interaction between DOX and either pristine graphene or GO with different ratios of oxygen-containing groups. The hydroxyl groups exhibited a stronger affinity for DOX than the epoxy groups. Therefore, the DOX loading capacity of graphene systems can be adjusted by increasing the ratio of hydroxyl to epoxy groups on the carbon surface.