Membrane-based method of washing and deacidification of oils, wherein a stream of oil is conveyed from an oil reservoir along one side of porous hydrophobic membrane, and washing aqueous solution is conveyed along another side of this membrane. The membranes form hollow fibers, and their total surface area and porosity are large enough for efficient removal of fatty acids, water, ions and hydrophilic organic impurities from oil. Membrane pore size is small enough, so that hydrodynamic mixing of oil and aqueous solution does not take place. Additional stabilization of oil/water meniscus in the pores is achieved by transmembrane pressure difference.