Thickness stretching effect based on shear and normal deformation theory is used in this paper for magneto-electro-elastic vibration analysis of a three-layered curved nanobeam including a nano core and two piezo-magnetic layers. Size-dependency is included in derivation of governing equations of motion based Eringen's nonlocal elasticity theory. The initial curvature is accounted in calculation of external works due to pre-mechanical, electrical and magnetic loads. The analytical method is presented to study the effect of significant parameters on the vibration characteristics. The numerical results are presented in terms of initial electro-magneto-mechanical loads, size-dependency parameter, opening angle, two parameters of Pasternak's foundation and core thickness to face-sheet thickness ratio.