A Coupling Magneto-Electro-Elastic (MEE) Node-based Smoothed Radial Point Inter-polation Method (CM-NS-RPIM) was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic (FGMEE) structures. By introducing the modi-fied Newmark method, the displacement, electrical potential and magnetic potential of the struc-tures under transient mechanical loading were obtained. Based on G space theory and the weakened weak (W2) formulation, the equations of the multi-physics coupling problems were derived. Using triangular background elements, the free vibration and transient responses of three numerical examples were studied. Results proved that CM-NS-RPIM performed better than the standard FEM by reducing the overly-stiff of structures. Moreover, CM-NS-RPIM could reduce the number of nodes while guaranteeing the accuracy. Besides, triangular elements could be gener-ated automatically even for complex geometries. Therefore, the effectiveness and validity of CM-NS-RPIM were demonstrated, which were valuable for the design of intelligence devices, such as energy harvesters and sensors.