In the present study, free vibration of sandwich flexoelectric plates resting on Pasternak foundation is investigated. The top and bottom layers are under applied voltage based on flexoelectricity considerations and core is a nanocomposite plate where reinforced by carbon nanotubes. Based on first-order shear deformation theory, flexoelectricity considerations and Hamilton’s principle, the governing equations are derived for the first time. Navier’s method is used to solve the governing equations analytically in the case of simply supported sandwich plate. Finally, the effects of different parameters are discussed in details. It is found when thickness of flexoelectric face sheets increase, the frequency of nano-sandwich plate decrease. The results of this study can be useful in design and manufacturing of flexoelectric systems as sensor and actuator.