In this study, the adsorption of doxorubicin (DOX), an anticancer drug, on pristine graphene (PG) and graphene oxide (GO) nanocarriers with different surface oxygen densities and in an aqueous environment with varying pH levels was investigated using molecular dynamics (MD) simulation. The drug loading and release on the GO nanocarrier was also simulated using pH as the controller mechanism. Overall, the DOX/nanocarrier interactions become stronger as the graphene surface oxygen density increases. Although pH has a negligible effect on the single-molecule drug adsorption on the GO surfaces under acidic and neutral conditions, significantly stronger DOX/nanocarrier interactions occur for the GO nanosheet with a lower surface oxygen density (GO-16, with an O/C ratio of 1 : 6) at basic pH levels. Moreover, the DOX/nanocarrier interactions are greatly weakened in the GO nanosheet with higher surface oxygen density (GO-13, with an O/C ratio of 1 : 3) under basic conditions. These observations are partly attributed to a more favorable geometry of the DOX molecule on the GO-16 surface as opposed to a loosely attached DOX molecule on the edges of the GO-13 nanosheet. When comparing the adsorption kinetics and transport properties of the DOX molecule in different GO systems, the drug diffusion coefficient increases with decreasing pH value (going from basic to neutral to acidic) due to the reduced total water-nanocarrier interactions. The latter observation is an indication of the more facilitated transport of the DOX molecule in an aqueous medium towards the nanocarrier surface at lower pH levels. Finally, we have confirmed the loading and release of the DOX molecules on the GO nanocarrier under neutral (pH = 7) and acidic (pH = 5) conditions, respectively. The former signifies the blood pH level, whereas the latter is reminiscent of the pH of a tumorous cell. The computational results presented in this work reveal the underlying mechanisms of DOX loading and release on PG and GO surfaces, which may be used to design better graphene-based nanocarriers for the DOX delivery and targeting applications.