  The radial part of Klein-Gordon equation is solved for the Woods-Saxon
potential within the framework of an approximation to the centrifugal barrier.
The bound states and the corresponding normalized eigenfunctions of the
Woods-Saxon potential are computed by using the Nikiforov-Uvarov method. The
results are consistent with the ones obtained in the case of generalized
Woods-Saxon potential. The solutions of the Schr\"{o}dinger equation by using
the same approximation are also studied as a special case, and obtained the
consistent results with the ones obtained before.
