Unveiling the characteristics of adsorption and diffusion of oxygen atoms on the surface of zirconium alloys at microscale is significant during the initial stages of zirconium oxide layer formation in PWRs or LWRs. In this work, Adsorption and diffusion of oxygen atoms on the surface of Zr and ZrO2 crystals have been investigated using molecular dynamic simulations. A special focus of this work is on the diffusion coefficient calculation based on our developed unbiased approach. The results show that a weak effect of temperature on the adsorption rate of ZrO2. The greater influence of grain boundary orientation than the concentration of Frenkel defects on the adsorption rate of oxygen atoms. The number of oxygen atoms that diffuse deep into the studied samples after adsorption on the free surface increases with increasing temperature. Moreover, for crystals that have a certain concentration of Frenkel defects in the volume, the diffusion coefficients are greater than for defect-free crystals. The diffusion coefficient of adsorbed oxygen atoms is smaller for crystal system with grain boundary of Zr/Zr. This distinct feature may be solving the experimental puzzle of oxidation rate of zirconium alloys under neutron irradiation.