Surface wave in half-infinite functionally graded magneto-electro-elastic materials is nvestigated. For convenience in the analysis, characteristics of the material are assumed to vary exponentially along the hickness direction. Based on the magneto-electro-elastic theory, a velocity equation of surface wave is derived under the open and short-circuit boundary conditions. The effect of material gradient coefficient on the wave velocity is studied. The computation results provide a basis for the development of new functionally graded magnetoelectroelastic devices.