A buckling analysis for a rectangular laminated composite plate with arbitrary edge supports subjected to biaxial compression loading was presented. The higher-order shear deformation theory was employed and a special displacement function, which could express an arbitrary edge support, was introduced into the Rayleigh–Ritz method. For the application of this analysis, the laminated composite plates with various edge supports were analyzed, and the buckling loads with these edge supports were obtained accurately. During these edge supports, particularly elastic edge support was simulated by three springs and reasonable results were obtained. Furthermore, the buckling modes were determined. The results show that the present method can be widely used to analyze the buckling behavior of composite plates with arbitrary edge conditions.