The numerical solutions of multi-group radiation diffusion equations are of great importance in the research of ICF simulations.The multi-group radiation diffusion equations consist of a set of diffusion equations of radiation, one ionic heat conduction equation and one electronic heat conduction equation.These equations are nonlinearly coupled, and usually solved by splitting source iteration methods.In this paper, convergence of the splitting source iteration method is analyzed.We focus on the splitting iteration step of the method and obtain convergence results.We also developed a new iteration method, which solves the multi-group radiation equations in a coupled manner.The new method is more efficient and shows very good stability.Numerical experiments and computations are presented and compared to the splitting source iteration.