The DV-X_α-Cluster molecular orbital method has been applied to investigate the mechanism of NO adsorption and dissociation at the oxygen vacancy of LaCoO₃ perovskite-type oxides. This study has been undertaken in order to design and develop the catalysts with high activities for the NO_x direct decomposition. It is indicated by calculation that when NO is adsorbed at the oxygen vacancy of LaCoO₃ catalyst, almost half of the 2π^* band in the adsorbed NO is occupied with electrons, because of the electron back donation from the catalyst to the 2π^* band of adsorbed NO. It is concluded that N-O bond becomes weak as NO adsorbs at the oxygen vacancy of LaCoO₃ catalyst at the primary step of NO decomposition.