Combining a detailed non-grey radiative transfer computation with the three dimensional hydrodynamics, we investigate a reliable numerical scheme for turbulent convection in the solar surface. The solar photosphere is the extremely turbulent region composed of partly ionized compressible gases in high temperature. Especially, the super adiabatic layer (SAL) near the solar photosphere is the shallow transition region where the energy transport varies steeply from convection to radiation. In order to describe physical processes accurately, a detailed treatment of radiative transfer should be considered as well as the high resolution computation of fluid dynamics. For a direct computation of radiation fields, the Accelerated Lambda Iteration (ALI) methods have been applied to hydrodynamical medium, incorporating the Opacity Distribution Function (ODF) as a realistic schemes for non-grey problems. Computational domain is the rectangular box of dimensions $42{ imes}3Mn$ with the resolution of $1202{ imes}190$ meshed grids, which covers several granules horizontally and 8 ~ 9 pressure scale heights vertically. During several convective turn-over times, the 3-D snapshots have been compiled with a second order accuracy. In addition, our radiation-hydrodynamical computation has been compared with the classical approximations such as grey atmospheres and Eddington approximation.