Multiferroic CoFe2O4–BiFeO3 (CFO–BFO) core–shell nanofibers were synthesized by coaxial electrospinning. The spinel structure of CFO and perovskite structure of BFO were confirmed by x-ray diffraction and high-resolution transmission electron microscopy. The core–shell configuration of nanofibers was verified by scanning electron microscopy and transmission electron microscopy images. The macroscopic ferromagnetic property of core–shell nanofibers was demonstrated by magnetic hysteresis loop. The local magnetoelectric (ME) coupling was confirmed by using dual frequency piezoresponse force microscopy (PFM) under an external magnetic field, showing magnetically induced evolution of piezoresponse and domain structure. The ferroelectric characteristics are demonstrated by the switching spectroscopy PFM. From PFM hysteresis and butterfly loops, it is observed that the piezoresponse amplitude is reduced while coercive voltage increased under external in-plane magnetic field, induced through the mechanical interactions between magnetostrictive CFO and piezoelectric BFO, from which the lateral ME coupling can be estimated quantitatively. The nanofibers thus can find a variety of applications as a one-dimensional multiferroic material.