Abstract: The thermal radiation problem within medium in engineering applications is a typical multiscale problem. Various gas kinetic schemes based on the Boltzmann transport equation have been widely used in the multiscale transient problems. In order to overcome the limitations of CFL conditions in the explicit solution, this article aims to solve the steady-state radiation transport equation through the gas kinetic scheme directly. The SDUGKS, which is developed from the core idea of discrete unified gas kinetic scheme(DUGKS) and applied to the calculation of steady-state problems, will be further extended to the calculation of multiscale steady-state heat radiation transport. The SDUGKS inherits the interface reconstruction implemented by the DUGKS along the characteristic line discretely, and realizes the correction of the radiation intensity through the unit update of implicit delta formulation. The radiation intensity asymptotically converges to the stable value by successive iteration methods. Several one-dimensional and two-dimensional thermal radiation problems were adopted. Compared with analytical solutions of special cases and available results by other numerical methods, the computational accuracy and efficiency of SDUGKS were tested, and its asymptotic preservation within multiscale condition was demonstrated.