A diffusion approximation equation was derived for steady radiative transport in graded index media. With discretization and finite element method, steady radiative heat transfer in two-dimensional rectangular gray semitransparent medium are examined to verify performance of the diffusion approximation. Cases with uniform index distribution and graded index distributions are considered. Boundary radiative heat flux and media temperature distribution under radiative equilibrium are determined with diffusion approximation and compared with results of radiative transfer equation. It shows that accuracy of the diffusion approximation is influenced by index, scattering characteristics,optical depth and scattering albedo. As the medium is optical thick and scattering is strong, the diffusion approximation shows good accuracy and can be considered as a rapid algorithm for steady radiative transfer problem in a semitransparent graded index medium.