Abstract: This paper investigates the propagation behaviors of shear horizontal waves in a functionally graded piezoelectric/piezomagnetic layered half-space with an imperfect interface. The so-called “spring”model is used to describe the interfacial properties, the properties of functionally graded piezoelectric materials are assumed to vary exponentially in the direction of the thickness, and the surface of the functionally graded piezoelectric layer is electrically open. The dispersion equations are derived, and numerical examples are provided to show the influences of the interfacial properties, the graded variation, and the thickness of the functionally graded piezoelectric layer on the phase velocity. The obtained results are of significance in applying functionally graded piezoelectric/piezomagnetic composites to acoustic wave devices.