In order to prepare parabolic superhydrophobic materials, copper meshes were used as the substrate and ultrasonic etching and oxidative corrosion were carried out with FeCl3 solution and H2O2 solution, respectively, and then the surface was modified with stearic acid (SA). The topological structure and surface wettability of the prepared mesh were characterized by fluorescence microscope, scanning electron microscopy and contact angle measurement. Finally, the as-prepared copper meshes were applied to oil-water separation. The results showed that the micro-nano-mastoid structure on the surface of the copper mesh was flaky bulges, forming a rough structure similar to a paraboloid. When the oxidative corrosion time of H2O2 was 1 min, it is more beneficial to increase the hydrophobicity of the surface of the copper mesh and increase the contact angle of water droplets on the surface of the membrane. Additionally, based on superhydrophobic materials of the parabolic copper mesh, the static contact angles of the water droplets, engine oil and carbon tetrachloride with the surface were approximately 153.6°, 5° and 0.1°, respectively and the sliding angle of the water droplets with the surface were approximately 4.9°. The parabolic membrane was applied to discuss the separation efficiency of different oils with deionized water and the separation efficiency was obtained as benzene > carbon tetrachloride > oil > machine oil. Therefore, based on the research, the parabolic superhydrophobic material has good efficiency of oil-water separation.