It is observed that the addition of Nb or Ge to Zr alloy can improve its corrosion resistance. Because of the extreme importance of the mechanism of oxidation to corrosion properties of Zr alloy, we systematically investigate the O adsorption properties on pure Zr surface and Zr surface with Nb or Ge using first-principle calculations based on density functional theory. Firstly, we present the absorption energies to reveal the influences of Nb and Ge on the O absorption capacity of Zr surfaces, resepctively. According to the calculated absorption energies, we find that Nb and Ge reduce the oxygen absorption capacities of most of surfaces, and the only exception is that Nb enhances the oxygen absorption capacity of Zr(1120) surface. Moreover, the absorption energy of O at favorable site on Zr(0001) surface is much lower than on Zr(1010) or (1120) surface. Therefore, the initial oxidation of polycrystalline Zr should occur at Zr(0001) surface and the absorption capacity of this surface takes a predominant role in the initial oxidation of polycrystalline surface. Secondly, the segregation of Nb or Ge in Zr alloy is anisotropic. We find that the segregation of Ge to surface is exothermic, while the segregation of Nb to surface is endothermic. Nb and Ge migrate to Zr(0001) surface more easily than to Zr(1120) and Zr(1010) surfaces. Therefore, the influence of Nb or Ge on absorption property of Zr(0001) is much larger than that of Zr(1010) or (1120) surface. Based on the adsorption and segregation properties of Nb and Ge on Zr surfaces, both Nb and Ge can reduce the oxygen absorption capacity of Zr surface and inhibit the initial oxidation of Zr alloy surface, which can be used to understand the experimental observation that Nb and Ge can improve the corrosion resistance of Zr alloy. Finally, the electronic structure analysis shows that the influences of Nb and Ge on oxygen adsorption capacity of Zr surface are exerted by changing the d-band distribution. According to Hammer-Norskov d-band center theory, the absorption energy of absorpate on transition metal surface is mainly determined by d-band center. The addition of Nb or Ge to the Zr surface changes the location of d-band of the surface, which results in the variation of absorption energy of O atom on the Zr surface. For absorption at top site on each surface, it is found that the absorption energy of O only depends on the d-band center of the surface atom below the O atoms. However, for absorption at favorable sites on each surface, the absorption energy of O atom is influenced not only by the d-band center of surface atom, but also by atomic structural properties of the surface.