Approximate bound state solutions of the Dirac equation with the Hulthen plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary l-state. The energy eigenvalue equation and the corresponding two-component wave function are calculated by solving the radial and angular wave equations within a recently introduced shortcut of the Nikiforov-Uvarov (NU) method. The solutions of the radial and polar angular parts of the wave function are given in terms of the Jacobi polynomials. We use an exponential approximation in terms of the Hulthen potential parameters to deal with the strong singular centrifugal potential term l(l + 1)r(-2). Under the limiting case, the solution can be easily reduced to the solution of the Schrodinger equation with a new ring-shaped Hulthen potential.