In this paper, an explicit fully discrete three-level pseudo-spectral scheme with rnalmost unconditional stability for the Cahn-Hilliard equation is proposed. Stabilrnity and convergence of the scheme are proved by Sobolev’s inequalities and the rnbounded extensive method of the nonlinear function (B.N. Lu[4] (1995)). The rnscheme possesses the almost same stable condition and convergent accuracy as the rnCreak-Nicloson scheme but it is an explicit scheme. Thus the iterative method rnto solve nonlinear algebraic system is avoided. Moreover, the linear stability of rnthe critical point u0 is investigated and the linear dispersive relation is obtained.rnFinally, the numerical results are supplied, which checks the theoretical results.