Understanding the interaction mechanism of the drug molecules on the nanostructured material's surface is crucial for the development of effective drug delivery systems. Motivated by the recent studies of the possible use of a carbon-based nanomaterial as a drug delivery substrate for the anticancer drug 5-fluorouracil (5FU) molecule, we systematically investigate the structural stability and electronic properties of the adsorption interaction of the 5FU molecule on the graphene oxide nanosheet (GON) surface by using density-functional theory (DFT) calculations. The optimized structural geometry, energetic and thermal stability, dipole moment, and charge transfer of the 5FU molecules adsorption on the GON surface were determined, while the electronic properties including band structures, density of states, wave functions, and electronic charge density were analyzed. We find that both the surface epoxy or hydroxyl groups of the GON can promote the adsorption of 5FU molecules on the surface, while the enhancement of the adsorption energy for the hydroxyl groups is greater than that for the epoxy groups on the surface. This phenomenon significantly alters electronic states from semiconductor to metallic via rehybridization orbitals mediated by oxygen functional groups. Therefore, our findings suggest that GON surfaces could serve as promising platforms for delivering the anticancer drug 5FU.