Heteroepitaxy of complex oxide thin films is a significant challenge when a large mismatch in the lattice parameters (>8%) and difference in the crystallographic symmetry coexist between the film and substrate. Herein, the heteroepitaxial growth of a hexagonal delafossite CuFeO₂ thin film with (00.1) orientation on a cubic perovskite (001) SrTiO₃ substrate through translational and rotational domain matching epitaxy is reported. The rotational in-plane domain orientation relationships are CuFeO₂ [11.0]//SrTiO₃ [110] and CuFeO₂ [21^-.0]//SrTiO₃ [110] with about 10% in-plane lattice mismatch. The 14.8 nm-thick (00.1) CuFeO₂ thin film shows high-crystalline quality with a full width at half maximum of rocking curve of about 0.24° and exhibits a possible indirect optical bandgap of 1.43 eV or direct optical bandgap of 1.94 eV. Herein, not only a model system demonstrating translational and rotational domain matching heteroepitaxy of complex oxides is reported, but also a way to thin-film heterostructures integrating hexagonal delafossite with cubic perovskite materials for functional oxide devices is opened.