Objective Piezoelectric materials are widely used in MEMS / NEMS due to their excellent electromechanical properties. A mathematical model of functionally graded piezoelectric FGP nanobeams including the flexoelectric effect and the piezoelectric effect was proposed to solve the problem that the flexoelectric effect and shear effect of piezoelectric materials at the microscale / nanoscale are neglected in the current calculation of the electromechanical response of piezoelectric nanostructures. The nanobeam consists of a piezoelectric layer and a functionally graded layer while the materials of the functionally graded layer follow the power-law exponential distribution. Methods Firstly based on Reddy?? s third-order shear deformation theory nonlocal strain gradient theory NSGT Hamilton?? s principle and Von Kármán geometric nonlinearity the nonlinear electromechanical coupling governing equations and corresponding boundary conditions of the gradient beam were obtained. Then the linear frequency nonlinear natural frequency and the root mean square RMS output voltage of the simply supported beam were obtained by combining the Runge-Kutta method and the Galerkin method. Results The presented model in this study was verified by existing literature results. In addition the numerical results showed that flexoelectric constants piezoelectric constants strain gradient parameters nonlocal parameters power-law index and geometric dimensions have an impact on the nonlinear natural frequency and RMS voltage. Conclusion Compared with the Euler beam theory and Timoshenko beam theory the gradient beam with the same mass has higher RMS voltage and lower nonlinear natural frequency when using Reddys third-order shear deformation theorK.