The bound eigenfunctions and spectrum of a Dirac hydrogen atom are found taking advantage of the SU (1, 1) Lie algebra in which the radial part of the problem can be expressed. For defining the algebra we need to add to the description an additional angular variable playing essentially the role of a phase. The operators spanning the algebra are used for defining ladder operators for the radial eigenfunctions of the relativistic hydrogen atom and for evaluating its energy spectrum. The status of the Johnson-Lippman operator in this algebra is also investigated.Key words: relativistic hydrogen atom, ladder operators, SU (1, 1) Lie algebra PACS: 33.10.C, 11.10.QrThe bound solutions of the hydrogen atom are of great importance in both classical and quantum mechanics and so is the search for new ways of solving or using such problem [1,2,3,4,5,6,7,8,9,10]. The purpose of this paper is to discuss an algebraic solution for the bounded eigenstates of the relativistic hydrogen