Controlling liquid adhesion is a fundamental issue in many applications for special wettable surfaces. Compared to superhydrophobic surfaces of different water adhesion, superoleophobic surfaces of controllable oil adhesion are much more practical, as it leads to non-wetting for both water and oil. However, previously the investigation for oil adhesion ability on superoleophobic surfaces in oil/air/solid system has been extremely rare. In this work, we describe a convenient approach to fabricate superoleophobic surfaces through perfluorothiolate reaction on Cu(OH)2 nanostructure surfaces and investigate their possible application in oil droplet transportation. The prepared surfaces exhibit controllable oil adhesive force depending on surface nanostructures or external preloads on the oil droplet. A model of the penetrating Cassie state is used to help analyze the unique phenomena on oil adhesion. Moreover, we provide a proof of demonstrate of oil transportation for application in oil-based microreactors via our surfaces. Our results give a useful attempt in understanding the fabrication principle of preparing superoleophobic surfaces with controllable oil adhesion.