  The Dirac equation, with position-dependent mass, is solved approximately for
the generalized Hulth\'{e}n potential with any spin-orbit quantum number
$\kappa$. Solutions are obtained by using an appropriate coordinate
transformation, reducing the effective mass Dirac equation to a
Schr\"{o}dinger-like differential equation. The Nikiforov-Uvarov method is used
in the calculations to obtain energy eigenvalues and the corresponding wave
functions. Numerical results are compared with those given in the literature.
Analytical results are also obtained for the case of constant mass and the
results are in good agreement with the literature.
