The group-diffusion equation in one-dimensional geometry is solved by using Green's function. In the first section, using Green's tensor, the group-diffusion equation is transformed into a system of linear equations which contain only the fluxes at the interfaces between the regions. Solving this equation, we obtain the fluxes at the interfaces and then the flux inside the regions with the aid of Green's tensor. This treatment is the same kind of approach as that of the response matrix method or the theory of invariant imbedding. In the second section, the group-diffusion equation is solved by the source iteration method. Using Green's function, the exact three-point difference equation is obtained and the explicit forms for the slab, cylindrical, and spherical geometry are given. It is shown that the usual three-point difference equation is obtained if the source term is approximated to be flat piecewise and if Green's function is expanded into Taylor's series neglecting all but the first two terms. Sample calculations for a thermal and a fast reactor show that the improved difference equation obtained by approximating the source term by a polynomial of second degree is more accurate than the usual three-point difference equation.