This paper investigates the propagation behavior of shear horizontal (SH) interfacial wave in a functionally graded piezoelectric(FGPE)/ functionally graded piezomagnetic(FGPM) bi-material with an imperfect interface, where the materials properties are assumed to vary exponentially at the direction normal to the interface. The so-called “spring” model is used to describe the mechanical property of the interface, namely the stresses are continuous along the interface while the mechanically displacements are noncontinuous. the interface is assumed electromagnetically permeable bonding and electromagnetically absorbent bonding. The dispersion equation of interface wave is derived in explicit form, and the numerical examples are provided to show that the different material combinations, the imperfect degree of the interface and the gradient variation of material constants on the phase velocity.