In recent years, both the increasing frequency of oil spill accidents and the urgency to deal seriously with industrial oil-polluted water, encouraged material scientists to design highly efficient, cost effective oil-water separation technologies. We report on electrospun nanofibrous membranes which are composed of core-sheath structured cellulose-acetate (CA)-polyimide (PI) nanofibers. On the surface of the CA-PI fibers a fluorinated polybenzoxazine (F-PBZ) functional layer, in which silica nanoparticles (SNPs) were incorporated, has been applied. Compared with F-PBZ/SNP modified CA fibers reported before for the separation of oil from water, the PI-core of the core-shell F-PBZ/SNP/CA-PI fibers makes the membranes much stronger, being a significant asset in their use. Nanofibrous membranes with a tensile strength higher than 200 MPa, a high water contact angle of 160 degrees and an extremely low oil contact angle of 0 degrees were obtained. F-PBZ/SNP/CA-PI membranes seemed very suitable for gravity-driven oil-water separation as fast and efficient separation (>99%) of oil from water was achieved for various oil-water mixtures. The designed core-sheath structured electrospun nanofibrous membranes may become interesting materials for the treatment of industrial oil-polluted water.