The development of efficient oil/water separation membranes is highly significant for reducing severe environmental pollution nowadays. Constructing hierarchical structures with double-scale roughness and inverted trapezoidal geometry is an alternative rational design to fabricate low oil-adhesive membranes. Based on this design concept, a Cu mesh vertically wrapped with novel microphone-like Cu-CAT-1 hierarchical microstructures with double-scale roughness was tactfully prepared by a local concentration effect, which was referred to as CCMOF. The CCMOF possessed superior anti-oil-fouling performance and an outstanding water-absorbing capacity (180.3% larger than that of the pristine Cu mesh) due to its ingenious microphone-like structures and its high affinity for water. Therefore, it could separate various types of oil/water mixtures with a considerably high flux of over 25,000 L m−2 h−1 and an extremely low oil content in filtrate of below 10 ppm. The design concept of this work offered a simple idea to design low oil-adhesive membranes for efficient oil/water separation.