We present exact solutions of the Dirac equation with equal vector and scalar potentials for pseudo Coulomb potential plus a new ring shaped potential. The Nikiforov Uvarov method is used to obtain analytical solutions of radial and angular wave functions of the Dirac equation. Simultaneously, energy spectrum equations are also obtained. It is shown that the radial and angular wave functions are respectively expressed by confluent hypergeogetric and universal associated Legendre functions.
