Based on the classical nonlinear plate theory, axisymmetric post-buckling behavior of a functionally graded circular plate is investigated under uniformly distributed radial compression. The governing equations are derived for the plate, and then a shooting method is employed to numerically solve the resulting differential equations. It is assumed that the thermal and mechanical properties of the functionally graded material vary varying continuously through the thickness of the plate, and follow a simple power law distribution of the volume fraction of the constituents. Axisymmetric post-buckling equilibrium paths for both clamped and simply supported plates are obtained. Also, variations of the central bending moments in the plate with the applied load are obtained after buckling of the plate. Furthermore, effects of the gradients of material properties and boundary conditions on the critical buckling load and post-buckling behavior of the functionally graded plates with different boundary conditions are discussed. Numerical results show that the post-buckling behavior of a functionally graded plate is different from that of homogenous plate, the gradients of material properties and the boundary conditions play important roles in analyzing post-buckling behavior of the functionally graded materials plates.