Separation of an oil and water mixture in an energy-saving approach is highly attractive for addressing both environmental and energy issues. To achieve this goal, this work reports a porous membrane (CR-PBz-FbM), which is made of a crosslinked electrospun polybenzoxazine fiber mat and exhibits gravity-driven continuous oil-water separation and pH-induced switches of oil-and water-selectivity. The membrane shows a toluene permeation flux of 21 750 L m(-2) h(-1) for immiscible oil-water separation, and a water permeation flux of 14 950 L m(-2) h(-1) after it has been turned from oil-selective to water-selective. The membrane still exhibits switching ability on the oil-and water-selectivity for separation of oil-water emulsions. Moreover, the CR-PBz-FbM membrane is mechanically robust and has high chemical stability. The attractive properties of the CR-PBz-FbM membrane lead to significant progress in oil-water separation from both environmental-protection and energy-saving viewpoints.