The buckling-like mechanical behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) structures is increasingly attracting research attention. However, buckling behavior has previously been studied separately as thermal buckling and mechanical buckling. In this context, this study investigates the buckling behavior of FG-GPLRC plates under combined thermal and mechanical loads. The coupled buckling problem is formulated according to the minimum potential energy theorem using first-order shear deformation theory (FSDT). In addition, the problem is approximated by the 2-D natural element method (NEM), and the resulting coupled eigen matrix equations are derived to compute the critical buckling temperature rise (CBTR) and the mechanical buckling load. The developed numerical method can solve thermal, mechanical, and coupled thermo-mechanical buckling problems, and its reliability is examined through convergence and benchmark tests. Using the developed numerical method, the buckling behavior of FG-GPLRC plates under thermal and mechanical buckling loads is examined in depth with respect to the key parameters. In addition, a comparison with functionally graded CNT-reinforced composite (FG-CNTRC) plates is also presented.