This report is on the synthesis by electrospinning of multiferroic core-shell nanofibers of strontium hexaferrite and lead zirconate titanate or barium titanate and studies on magneto-electric (ME) coupling. Fibers with well-defined core-shell structures showed the order parameters in agreement with values for nanostructures. The strength of ME coupling measured by the magnetic field-induced polarization showed the fractional change in the remnant polarization as high as 21%. The ME voltage coefficient in H-assembled films showed the strong ME response for the zero magnetic bias field. Follow-up studies and potential avenues for enhancing the strength of ME coupling in the core-shell nanofibers are discussed.