Research is being carried out worldwide for possible treatment of cancer. Graphene has been studied as a drug carrier for various cancer-related drugs [1-2]. In the present work, we apply theoretical models to study the electrons interactions, thermodynamic properties, and solvent interaction of the drug-carrier configuration. The stability of graphene means that it can be a nanocarrier in the biological system. The simulations result shows that graphene provides a stable base, where gemcitabine is a highly dissolvable and reactive drug. The adsorption of gemcitabine on the graphene was physical. The drug carrier configuration formed a highly impactful drug-carrier design.