.　This　paper　is　concerned　with　the　numerical　approximation　to　the　one-dimensional　Cahn-Hilliard　equation　with　time　periodic　solution.　We　adopt　the　implicit　Euler　method　and　the　spectral　Galerkin　method　for　the　temporal　and　spatial　discretization,　respectively.　Then　the　error　estimates　are　proved　for　both　the　semi-discrete　and　the　fully　discrete　schemes.　Numerical　experiments　are　carried　out　to　confirm　our　theoretical　results.