In this paper, the analytically bound state solution of the Dirac equation is obtained for the linear combination of the Manning-Rosen and Yukawa potentials by using Nikiforov-Uvarov method. To overcome the difficulties arising in the case for arbitrary k in the centrifugal part of the Manning-Rosen potential plus the Yukawa potential for bound states, we applied the developed approximation. Analytical expressions for the energy eigenvalue and the corresponding spinor wave functions for an arbitrary value k spin-orbit, radial n and l orbital quantum numbers are obtained. The relativistic energy eigenvalues and corresponding spinor wave functions have been obtained for case exact pseudospin symmetry by using the Nikiforov-Uvarov method. Furthermore, the corresponding normalized eigenfunctions have been represented as a recursion relation in terms of the Jacobi polynomials for arbitrary k states. A closed form of the normalization constant of the wave functions is also found. It is shown that the energy eigenvalues and eigenfunctions are very sensitive to k spin-orbital quantum number.