We investigate the magnetoelectric effect and potential fields of functionally graded multiferroic fibrous composites under anti-plane shear deformation coupled to in-plane electric and magnetic fields. The cylinders are exponentially graded along the radial direction. Rayleigh’s formalism and composite cylinder assemblage model are generalized to account for the configuration. We find that the grading parameter has a dramatic effect on the potential field of the inclusion and the effective property of the composite. We adopt this approach to numerically study the exponentially graded BaTiO 3--CoFe 2O 4 composite and provide insights into developing new multiferroic fibrous media with high magnetoelectric coupling.