The first-principles calculations of the diffusion processes of oxygen in pure Ni and Ni-Cr binary alloy are conducted to understand the oxidation behavior of nickel base alloys. The cohesive energy, insertion energy of atomic oxygen, and vacancy formation energy in nickel are calculated and compared with experimental data. The activation energies of oxygen are also calculated. The results show agreement with previous work for the oxygen diffusion in pure nickel. However, the calculated activation energy for the diffusion of oxygen in Ni-Cr binary alloy showed lower values than that in nickel because of the limitations of the current calculation model.