We solved the Dirac equation using the modified factorization method with the shifted Tietz-Wei potential model. Relativistic and non-relativistic ro-vibrational energy spectra were obtained as well as numerical solutions for different diatomic molecules ( , , and ). The eigenfunction for this potential has been obtained in terms of hypergeometric function. The energy variations were discussed graphically for different parameters of the shifted Tietz-Wei potential. Our results are in good agreement with the ones available in the literature.