Core-sheath multiwalled carbon nanotube (MWNT)-cellulose fibers of diameters from several hundreds of nanometers to several micrometers were prepared by coaxial electrospinning from a nonvolatile, nonflammable ionic liquid (IL) solvent, 1-methyl-3-methylimidazolium acetate ([EMIM][Ac]). MWNTs were dispersed in IL to form a gel solution. This gel core solution was electrospun surrounded by a sheath solution of cellulose dissolved in the same IL. Electrospun fibers were collected in a coagulation bath containing ethanol-water to remove the IL completely and dried to form core-sheath MWNT-cellulose fibers having a cable structure with a conductive core and insulating sheath. Enzymatic treatment of a portion of a mat of these fibers with cellulase selectively removed the cellulose sheath exposing the MWNT core for connection to an electrode. These MWNT-cellulose fiber mats demonstrated excellent conductivity because of a conductive pathway of bundled MWNTs. Fiber mat conductivity increased with increasing ratio of MWNT in the fibers with a maximum conductivity of 10.7 S/m obtained at 45 wt % MWNT loading.