The governing partial differential equations (PDEs) are deduced from the asymptotically correct, geometrically nonlinear theory to research the bucking and mode jumping behavior of biaxially antisymmetric angle-ply composite laminates. The PDEs are transformed into a system of nonlinear ordinary differential equations (ODEs) by using the generalized Galerkin method. Then, the post-buckling behavior is analyzed by using the solution extension software. At last, the paths of buckling mode jumping and critical loads for the composite laminates under the in-plane boundary condition of straight edge are determined. An example of 4-layer composite laminates shows that the numerical results in the primary post-buckling region from the present method agree with the finite element analysis (FEA); while the FEA may lose its convergence when solution comes close to the secondary bifurcation point, the analytic method has the capability to explore deeply into the post-secondary bucking realm and capture the mode jumping phenomenon.