In this study ، Cytarabine anticancer drug approached fullerene C20 and variations in the chemical properties and reactivity of Cytarabine (anti-cancer drug) the thermodynamic parameters of the formation of nano-derivatives of the Cytarabine with the fullerene C20 nanostructure were calculated. For this purpose, seven states proposed for the formation of nano-derivatives ، all compounds were geometric optimization. Then, the calculations for determining the thermodynamic parameters at a temperature range of 298.15° K to 103.10° K (every one degree) and at a constant pressure of 1 atm and gas phase as well as the aqueous solvent phase is done. All calculations were performed using the B3LYP density functional theory method and the 31G-6* base series using Gaussian, Nanotube Modeler, Gauss view and Spartan software. It was found the optimal temperature for the synthesis of both water and gas phase is 298° K. According to the calculations carried out in the gas phase, the adsorption of V isomer is more likely, but in the aqueous solvent phase, the adsorption of the VI isomer is more probable.