The asymptotic perturbation method is used to deal with the Cahn-Hilliard equation and obtain the inner and outer solutions of traveling waves. The two solutions are matched into one solution of the equation. The feature of the method not only matches the inner and outer solutions of the higher order partial differential equation, but also satisfies the boundary condition and initial condition. After a long time evolution, the solutions of the Cahn-Hillard equation have the structures of traveling waves as the limit states. The result in this paper can explain the theoretic and numerical simulation results of the Cahn-Hillard equation. The property of model fits well with that of the equation.