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In this study, using the application of density functional theory, the mechanism of graphene-NiNx (x = 1, 2, 3, 4) series non-noble metal catalysts in acetylene hydrogenation was examined under the B3LYP/6-31G** approach. With the DFT-D3 density functional dispersion correction, the effective core pseudopotential basis set of LANL2DZ was applied to metallic Ni atoms. The reaction energy barriers of NiNx catalysts are different from the co-adsorption structure during the catalytic hydrogenation of graphene-NiNx (x = 1, 2, 3, 4). The calculated results showed that the energy barrier and selectivity of graphene-NiN4 for ethylene production were 25.24 kcal/mol and 26.35 kcal/mol, respectively. The low energy barrier and high activity characteristics showed excellent catalytic performance of the catalyst. Therefore, graphene-NiN4 provides an idea for the direction of catalytic hydrogenation.