For the propagation of horizontally shear waves (SH-waves) in a functionally gradient piezoelectric material (FGPM) plate, the governing equations are established by the theory of elasticity. The Airy equations and Airy functions are applied to find the solutions of the equations. Numerical results indicate that: compared with those of SH-waves in a transversely isotropic piezoelectric plate, remarkable difference can be observed for the dispersion properties of SH-waves in a FGPM plate. Material coefficients gradient variation patterns do not affect higher modes dispersion properties of SH-waves in a FGPM plate for electrically open case. While for electrically shorted case, dispersion properties of SH-waves higher modes are affected by the material coefficients gradient variation patterns, remarkable influences can be observed for S0 mode. Influences of materials coefficients gradient variation patterns on cutoff-frequencies of SH-waves are also revealed. The results obtained are meaningful for the investigation and characterization of SH-waves in inhomogeneous media.