The elastoplastic buckling behaviors of functionally graded material (FGM) beams under axial compression loading are studied in consideration of temperature dependence of material properties. Firstly, elastoplastic material properties are obtained on the basis of bilinear hardening model and temperature dependence, meanwhile the elastoplastic constitutive equations of the FGM are established as well. Then introducing the Hamilton principle, the elastoplastic buckling behaviors of FGM beams are transformed into solving the eigenvalues in symplectic space. At the same time, the buckling critical loads corresponding to the generalized eigenvalues of the canonical equations can be calculated by the bifurcation conditions. Finally, the elastoplastic buckling characteristics and solution process of them are revealed by the symplectic method and effects of material gradient, geometrical parameters of structure and ambient temperature on the critical loads of elastoplastic buckling are discussed in detail. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.