In the present study we propose a more promising catalyst for the deNOx process to eliminate harmful nitrogen oxides from the environment. The study was performed with a computer calculation using density functional theory (DFT) based on an ab initio method. Two zeolite catalysts, FAU and MFI, were selected with additional Cu-O-Zn bimetallic dimer adsorbed inside the pores of both zeolites. Based on the analysis of preliminary studies, the most probable way of co-adsorption of nitric oxide and ammonia was selected, which became the initial configuration for the reaction mechanism. Two types of mechanisms were proposed: with hydroxyl groups on a bridged position of the dimer or a hydroxyl group on one of the metal atoms of the dimer. Based on the results, it was determined that the FAU zeolite with a bimetallic dimer and an OH group on the zinc atom was the most efficient configuration with a relatively low energy barrier. The real advantage of the Cu-Zn system over FAU and MFI in hydrothermal conditions has been demonstrated in comparison to a conventional Cu-Cu catalyst.