Fission of simple metal clusters is investigated using a jellium model which allows axial symmetrical deformations and fission. The Kohn-Sham equations for the jellium model are solved by the discrete-variable representation method where the zeros of the sine functions and the zeros of the 0th order Bessel functions are used for the basis for z-coordinate and ρ-coordinate, respectively. The comparison between the jellium model results and the shell-correction method results is made.