Abstract <p>With the structure size entering the micron/nanometer scale, the mechanical properties of materials show a significant size-dependent effect. Functionally graded graphene origami expanded metamaterials (FG-GOEAM) have become a focal point of interest because of their outstanding mechanical performance. Although the mechanical behavior of FG-GOEAM in beams, plates, and shell structures has been extensively studied, the research for FG-GOEAM microbeams within the framework of the modified strain gradient theory is still insufficient, especially in terms of the thermal environmental effects. To fill this research gap, this paper combines the modified strain gradient theory with the refined beam theory for the first time to investigate the buckling and free vibration characteristics of FG-GOEAM microbeams. Describing thermal loads in terms of thermal strain energy, and the material parameters are simulated using a micromechanical model assisted by genetic programming (GP). The governing equations are based on the Lagrange equations and solved by the Chebyshev–Ritz method. The effects of size effect parameters, temperature, graphene distribution mode, folding mode, weight fraction, folding degree, length-to-fineness ratio, and boundary conditions on the mechanical properties of the microbeams are comprehensively investigated. The results show that the reasonable design of the FG-GOEAM distribution pattern and optimization of reinforcement material content can significantly enhance the microbeam performance. The proposed method also provides an effective solution for analyzing the buckling and vibration behaviors of microbeams with advanced materials.</p>