  In this work, the analytical solution of the hyper-radial Schr\"{o}dinger
equation for the spherical Woods-Saxon potential in D dimensions is presented.
In our calculations, we have applied the Nikiforov-Uvarov method by using the
Pekeris approximation to the centrifugal potential for arbitrary $l$ states.
The bound state energy eigenvalues and corresponding eigenfunctions are
obtained for various values of $n$ and $l$ quantum numbers.
