This study presents the solutions of the Dirac equation with a new suggested Yukawa-type potential for any spin-orbit quantum number kappa interacting with a Coulomb-like tensor interaction. In the presence of spin and pseudospin (p-spin) symmetries, the approximate energy eigenvalues and wave functions are obtained by means of the parametric Nikiforov-Uvarov (pNU) method and the asymptotic iteration method (AIM). The numerical results show that the Coulomb-like tensor interaction removes degeneracies between spin and p-spin state doublets. The bound state solutions of the Schrodinger and Klein-Gordon equations for this new potential have also been presented. Our analytical results are in exact agreements with previous works. (C) 2013 Elsevier Inc. All rights reserved.