  The Klein-Gordon equation is solved approximately for the Hulth\'{e}n
potential for any angular momentum quantum number $\ell$ with the
position-dependent mass. Solutions are obtained reducing the Klein-Gordon
equation into a Schr\"{o}dinger-like differential equation by using an
appropriate coordinate transformation. The Nikiforov-Uvarov method is used in
the calculations to get an energy eigenvalue and and the wave functions. It is
found that the results in the case of constant mass are in good agreement with
the ones obtained in the literature.
