We report the epitaxial thin-film synthesis of SrCu3O4 with infinitely stacked Cu3O4 layers composed of edge-sharing CuO4 square planes, using molecular-beam epitaxy. Experimental and theoretical characterizations showed that this material is a metastable phase that can exist by applying tensile biaxial strain from the (001)-SrTiO3 substrate. SrCu3O4 shows an insulating electrical resistivity in accordance with the Cu2+ valence state revealed by X-ray photoelectron spectroscopy. First-principles calculations also indicated that the unoccupied d3z2-r2 band becomes substantially stabilized owing to the absence of apical anions, in contrast to A2Cu3O4Cl2 (A = Sr, Ba) with an A2Cl2 block layer and therefore a trans-CuO4Cl2 octahedron. These results suggest that SrCu3O4 is a suitable parent material for electron-doped superconductivity based on the Cu3O4 plane.