Abstract: We discuss numerical simulation of one-dimensional non-equilibrium radiation diffusion equations.A weighted numerical flux between adjacent grid cells is obtained by solving heat conduction equation with discontinuous coefficient.With this numerical flux of diffusive generalized Riemann problem(dGRP),a discontinuous finite element method is proposed for radiation diffusion equations. A backward Euler time diseretization is applied for semi-discrete form and a Picard iteration is used to solve nonlinear system of equations.Numerical results demonstrate that the method has a capability of capturing strong gradients and can be accommodated to discontinuous diffusion coefficient.