Based on the Hamiltonian principle and taking nonlocal effect, piezoelectric effect and flexoelectric effect into consideration, the vibration governing equation and boundary conditions of the Timoshenko nano-beam in the viscoelastic medium were established, and the method of solving the governing equation of flexoelectric nano-beam with simply supported boundary conditions was adopted. The effects of nonlocal parameters, flexoelectric effect and viscoelastic medium on the vibration characteristics of the flexoelectric nano-beam were systematically studied. The results show that the transverse flexoelectric coefficient can significantly increase the structural stiffness of the flexoelectric nano-beam, while the nonlocal parameters and the tangential flexoelectric coefficient can reduce the structural stiffness of the system. In addition, the critical damping coefficient of the viscoelastic medium, in which the flexoelectric nanobeam no longer reciprocating vibration, can be obtained by studying the effects of viscoelastic medium. Research results can provide a theoretical basis for the extension and application of flexoelectric nano-beam in energy harvester.