We　investigate　the　boundary　layer　effects　of　the　3-D　incompressible　Boussinesq　system　for　Rayleigh-Benard　convection　with　vanishing　diffusivity　limit.　By　adopting　the　multi-scale　analysis　and　the　asymptotic　expansion　methods　of　singular　perturbation　theory,　we　construct　an　exact　approximating　solution　for　the　viscous　and　diffusive　Boussinesq　system　with　well-prepared　initial　data.　In　addition,　we　obtain　the　convergence　result　of　the　vanishing　diffusivity　limit.