In this paper, a refined higher-order theory was developed which can accurately calculate the electromechanical behavior of laminated structures with piezoelectric layer (LSP) and functional gradient sandwich structures with piezoelectric layer (FGSSP). The Reddy-type global-local higher-order theory (RGLHT) was used in the displacement field, which satisfies continuity conditions of displacements and stresses at interfaces and the free surface boundary conditions. Layerwise theory was used in the potential field, which means that for structures with thin piezoelectric layers, the potential can be assumed to be linear distribution through the thickness direction. With the use of Hamilton's principle and active control principle, the motion control equation of functional gradient structures with piezoelectric layer with damping was derived. Based on the refined higher-order theory, an isogeometric analysis (IGA) method was constructed. Firstly, the bending behavior of a LSP was analyzed, so that the effectiveness of the refined higher-order theory has been verified. Subsequently, influence laws of ply angles and functional gradient coefficients on the bending behavior of a FGSSP was further investigated, in which the deflection at the center point of the structure decreases with increase of the ply angles or the functional gradient coefficients. When the functional gradient coefficients are taken from 0 to 5, influence of the functional gradient coefficients on bending behavior is more significant than that of the ply angles. Finally, the dynamic response of an undamped functional gradient structure with piezoelectric layer was analyzed. The results indicated that when the speed feedback gain coefficient of the system is zero, the structure will oscillate without attenuation. When the gain coefficient of velocity feedback is increased, the attenuation of structural oscillation amplitude is accelerated, and the time required for attenuation is decreased, so the active control of forced vibration of the undamped structure was achieved by adjusting the speed feedback gain coefficient.