As an important class of functional materials, the multiferroic piezoelectric/piezomagnetic nanocomposites are widely used in sensors and actuators of advanced functional devices. The interface effects have become a key issue in designing and regulating the physical properties of such nanocomposites. This paper investigates the magneto-electro-elastic (MEE) responses for multiferroic fibrous nanocomposites with imperfectly bonded interface under far-field anti-plane shear and in-plane electric and magnetic loadings. On this basis, the analytical solutions of the effective MEE moduli of the multiferroic nanocomposites are obtained by using a generalized self-consistent method combined with the complex variable method. The present analytical solutions considering the nanointerface stresses and imperfect interface effect are verified by comparing with existing analytical solutions for simplified problem. Numerical analysis is conducted for different types of composite materials, and the effect of nanointerface stresses, imperfect interface parameters and volume fraction on the six components of MEE effective modulus is discussed in detail. The proposed theoretical estimation of effective moduli has certain theoretical value for the design and optimization of multiferroic nanocomposites.