Display omitted •Acetylene hydrogenation over FexOy clusters are theoretically investigated.•Acetylene hydrogenation over 5FeO cluster is impossible for the high energy barrier.•Acetylene hydrogenation to ethane over Fe2O3 cluster is kinetically most favorable. The acetylene hydrogenation reaction over FeO, Fe2O3 and Fe3O4 clusters are theoretically investigated, via C2H2 adsorption, approach of molecular H2 to cluster, H2 dissociation on FeO bond, and the sequential addition reaction of H atom. Over FeO cluster, the extremely high barrier for the addition reaction of H atom adsorbed on O atom (of cluster) predicts the impossible acetylene hydrogenation. Over Fe2O3 cluster, the overall barriers for H2 dissociation, addition reaction of two hydrogen atom are respectively 26.6, 32 and 31.8 kcal·mol−1 during the acetylene hydrogenation to form ethylene and 26.5, 35.5 and 9.1 kcal·mol−1 for its further hydrogenation to produce ethane. During the further hydrogenation pathway, the migration of semi-hydrogenated product C2H3 requires extra energy of 30.7 kcal mol−1. These barriers are lower than those of the pathways over Fe3O4 cluster. Hence, among three FexOy clusters, hydrogenation of acetylene to produce ethane on Fe2O3 cluster is kinetically most favorable.