This paper investigates waves propagating in a piezoelectric ceramic half-space with a thin functionally graded piezoelectric film and an air gap between the ?lm and the half-space. The material properties of the thin piezoelectric film vary exponentially in the direction perpendicular to the interfaces. By using the continuous conditions at the interfaces, the dispersion equations are given in determinant form. Based on the dispersion equations, the numerical examples are presented to show the effects of variations of material properties, piezoelectric layer thickness and different combinations of materials on the phase velocity. The obtained results are useful for the application of functionally graded piezoelectric materials to acoustic wave devices such as plate resonators, filters and sensors.