  The energy levels of hydrogen-like atom on a noncommutative phase space were
studied in the framework of relativistic quantum mechanics. The leading order
corrections to energy levels 2S_{1/2}, 2P_{1/2} and 2P_{3/2} were obtained by
using the \theta and the \bar\theta modified Dirac Hamiltonian of hydrogen-like
atom on a noncommutative phase space. The degeneracy of the energy levels
2P_{1/2} and 2P_{3/2} were removed completely by \theta-correction. And the
\bar\theta-correction shifts these energy levels.
