Based on the three-dimensional piezoelectric-semiconductor (PSC) and first-order shear-deformation theories, and considering the coupling extension, flexure, and shear deformations, a buckling model for a one-dimensional functionally graded PSC extension-flexure beam was established. The stability of a functionally graded PSC extension-flexure beam under an axial load was analyzed via the finite element analysis software COMSOL, and the first three critical buckling loads and distributions of the electromechanical field for a simply supported beam were obtained. The influences of the beam length-height ratio, initial electron concentration, and functionally graded parameters on the critical buckling loads are discussed based on some numerical examples.