The first doubly magic nucleus with the first closed shell, 1s_(1/2), is the ^4He isotope, and the understanding of its structure is very important. Hence, in this paper, we study the ^4He isotope composed of two deuteron clusters and consider the central Woods-Saxon potential between them. We selected the Dirac equation and solved it for this model using the Nikiforov-Uvarov method. At the end, the ground state energy and wave function of the isotope ^4He have been determined, and the results are compared with the experimental data. We obtained good values, and this proves that our model has a good prediction for the ground state.