The 1,3-dipolar cycloaddition of the aryl azide and some its of derivatives with cyclohex- 2-en-1-one was studied theoretically using different methods of Density Functional Theory (DFT): B3LYP, B3PW91, MPW1PBE, MPW1PW91 and M062X with the basic set 6-31g(d). Most of the used levels of theories provide closed results qualitatively, and the results of the level of theory M062X / 6-31g (d) show that these reactions in the gas state are spontaneously to form two products, but all the reactions are very slow and one of the products P1 is more spontaneous and faster than the other P2 , and when these reactions were studied with different solvents, it is found that solvents to have no actual effects on the rates of these reactions. The results of the level of theory M062X / 6-31g (d) indicate that the Gibbs free energy of the reactions for the substitutes of Aryl increases in negative values in order of 2,6-Cl, -4 NO2, 4-OCH3, 3-OCH3, 3-Cl, 2 -Cl, H-; i.e., the substitutes do not have a significant effect on the spontaneity of reactions compared to the substitute-H. It was observed that TS-P1 transition state energy for all substitutes was lower than TS-P2 transition state energy.