We study the effect of spatially-dependent mass function over the solution of the Dirac equation with the Coulomb potential in the (3 + 1)-dimensions for any arbitrary spin-orbit kappa state. In the framework of the spin and pseudospin symmetry concept, the analytic bound state energy eigenvalues and the corresponding upper and lower two-component spinors of the two Dirac particles are obtained by means of the Nikiforov-Uvarov method, in closed form. This physical choice of the mass function leads to an exact analytical solution for the pseudospin part of the Dirac equation. The special cases kappa = +/- 1(l = (l) over bar = 0; i.e., s-wave), the constant mass and the non-relativistic limits are briefly investigated. (C) 2010 Elsevier Inc. All rights reserved.