This paper aims to predict the substituent and Lewis acid catalysis effect or reactivity on the regioselectivity of (4+2) cycloaddition reaction of the substituted-E-arene-diazocyanides and nitrosobenzenes. Frontier orbital theory (FMO) has been applied to thermal and catalyzed Diels-Alder reaction by means of CNDO/2 and EHT-SPD methods. It has been found that: (1) The above reaction is positive rho(${ ho}$) values in Hammett equation, so it takes normal electron demand reaction, and four-frontier orbitals and Anh methods are identical with experimental major regioisomer.(2) When electron withdrawing radicals are substituted HOMO and LUMO energies of dienophiles are reduced, and the reactivity is increased. (3) The major regioisomer is predicted as B type, as the Lewis acid makes complexes of dienophile, and polaries LUMO coefficients of dienophile in an opposite way. (4) The linear correlation of Hammett is indicated in the graph of stabilized energies(${Delta}$E) and sigma(${sigma}$).