We report a convenient route to fabricate superoleophobic surfaces (abridged as SOS) on copper substrate by combining a two-step surface texturing process (first, the substrate is immersed in an aqueous solution of HNO3 and cetyltrimethyl ammonium bromide, and then in an aqueous solution of NaOH and (NH4)2S2O8) and succeeding surface fluorination with 1H,1H,2H,2H-perfluorodecanethiol (PFDT) or 1-decanethiol. The surface morphologies and compositions were characterized by field emission scanning electron microscopy and X-ray diffraction, respectively. The results showed that spherical micro-pits (SMP) with diameter of 50-100 μm were formed in the first step of surface texturing; in the second step, Cu(OH)2 or/and CuO with structures of nanorods/microflowers/microballs were formed thereon. The surface wettability was further assessed by optical contact angle meter by using water (surface tension of 72.1 mN m(-1) at 20°C), rapeseed oil (35.7 mN m(-1) at 20°C), and hexadecane (25.7 mN m(-1) at 20°C) as probe liquids. The results showed that, as the surface tension decreasing, stricter choosing of surface structures and surface chemistry are required to obtain SOS. Specifically, for hexadecane, which records the lowest surface tension, the ideal surface structures are a combination of densely distributed SMP and nanorods, and the surface chemistry should be tuned by grafted with low-surface-energy molecules of PFDT. Moreover, the stability of the so-fabricated sample was tested and the results showed that, under the testing conditions, superhydrophobicity and superoleophobicity may be deteriorated after wear/humidity resistance test. Such deterioration may be due to the loss of outermost PFDT layer or/and the destruction of the above-mentioned ideal surface structures. For UV and oxidation resistance, the sample remained stable for a period of 10 days.