The　main　purpose　of　this　paper　is　to　study　the　initial　layer　problem　and　the　infinite　Prandtl　number　limit　of　Rayleigh-Benard　convection　with　an　ill　prepared　initial　data.　We　use　the　asymptotic　expansion　methods　of　singular　perturbation　theory　and　the　two-time-scale　approach　to　obtain　an　exact　approximating　solution　and　the　convergence　rates　O　(epsilon(3/2))　and　O(epsilon(2)).