Due to the strong size-dependent property, flexoelectricity is one of the most advantageous applications of piezoelectricity on the micro/nano scale energy harvesting. However, rare researches have been conducted on energy harvesters composed by functionally graded flexoelectric materials (FGFMs). In this paper, the nonlinear vibration of a FGFMs energy harvesting nanobeam with a concentrated mass located at free end is analyzed theoretically while considering the electromechanical coupling effect induced by strain gradients. By referring to the Galerkin’s method, the corresponding equations of the coupled system and the approximated closed-form solutions of the electric and the power output are obtained. (nhnhanh)