Abstract: A Mode-Ⅲ crack inclined to an imperfect interface in piezoelectric phase of a bi-layered magnetoelectric composite was studied. A coupled interfacial imperfection model was proposed to characterize the imperfect interface. Fourier integral transform was applied to reduce the condition on the crack surface to a singular integral equation, which can be numerically solved by Lobatto-Chebyshev collection method for the stress intensity factor(SIF). The effects of the interfacial imperfection parameters, material constants, layer thickness, inclined angle, distance between crack tip-a and interface on SIF were systematically discussed. Several conclusions are yielded:the mechanical imperfection can enhance the SIF independently, while the magnetic or electric imperfection can reduce the SIF only through its coupling with the mechanical imperfection; the coupling of mechanical-magneto or mechanical-electro imperfection can reduce the SIF, but the magneto-electro imperfection coupling does not affect SIF in any case; the SIF can be reduced by changing material constants, such as increasing the shear moduli of piezomagnetic layer, decreasing the shear moduli and dielectric coefficient or increasing the piezoelectric coefficient of piezoelectric layer; the variation of SIF versus inclined angle or distance between crack tip-a and interface can be influenced by interfacial imperfection; increasing the thickness of piezomagnetic or piezoelectric layer can reduce the SIF in a finite interval.