This study presents analysis of nonlinear vibration of functionally graded (FG) micro-beams subjected to axial compressive load and resting on elastic foundation in framework of the Euler-Bernoulli beam theory (EBT) and nonlocal strain gradient theory (NSGT). The FG micro-beam composed of two materials including metal and ceramic is considered in which, the material properties change according to a simple power law of the coordinate in the thickness direction. The expressions of nonlinear frequencies of the FG micro-beams with simply-supported (S-S) and clapmed-clamped (C-C) boundary conditions are obtained in the analytical forms. The accuracy of the obtained results for the FG micro- beams is verified by comparing the obtained solutions with the published ones. Influences of some important parameters on the nonlinear vibration responses of the FG micro-beams are examined and discussed.