The oxygen adsorption on the Zr(0 0 0 1) surface is studied using first-principles total-energy calculations. The calculations are performed in the framework of density-functional theory and pseudopotential theory. We compare results obtained with the LDA including generalized gradient corrections (GGCs). We calculate the atomic structure and heat of adsorption for oxygen occupying various sites for coverage 1/4 less than or equal to Theta less than or equal to 1. We find that the energetic hierarchy of the different adsorption sites tested depend on non-local exchange-correlation effects. We also discuss the subsurface three domains model as proposed by Wang from LEED analysis [Surf. Sci. 343 (1995) L1167]. At the end, relaxation of the zirconium interlayer spacings is discussed as a function of the oxygen concentration and in terms of GGCs.