An exact three-dimensional analysis is presented for a functionally gradient piezoelectric material rectangular plate that is simply supported and grounded along its four edges. The state equations of the functionally gradient piezoelectric material are developed based on the state space approach. Assuming that the mechanical and electric properties of the material have the same exponent-law dependence on the thickness-coordinate, we obtain an exact threedimensional solution of the coupling electroelastic fields in the plate under mechanical, and electric loading on the upper and lower surfaces of the plate. The influences of the different functionally gradient material properties on the structural response of the plate to the mechanical and electric stimuli are then studied through examples.