A banded matrix iterative approach is applied to study scattering of a TE incident wave from a perfectly conducting one-dimensional random rough surface. It is much faster than the full matrix inversion approach or the conjugate gradient method. When compared to the Kirchhoff iterative approach, it is of comparable CPU time, and works for cases when the Kirchhoff iteration is erroneous. The method is illustrated for a variety of parameters with particular application to large scale rough surface problems. The largest surface length used is 400 wavelengths with 3200 unknowns, and all the coherent wave interactions are included within the entire surface length. The accuracy of the banded iterative approach is demonstrated by showing that the results overlie those of the exact matrix inversion and the conjugate gradient method. The numerical method is also easy to implement. With this approach, we are able to compute the new response characteristics of composite rough surfaces with much larger scales. The case of large incidence angle is also studied. Comparison is also made with the analytic second-order Kirchhoff theory.