We report the results of growth kinetics of oxidation process on niobium thin film surfaces exposed to air at room temperature by using a surface sensitive non-destructive X-ray reflectivity technique. The oxidation process follows a modified Cabrera-Mott model of thin films. We have shown that the oxide growth is limited by the internal field due to the contact potential which develops during the initial stage of oxidation. The calculated contact potential for 100 and 230 angstrom thick films is 0.81 +/- 0.14 and 1.20 +/- 0.11V respectively. We report that 40% increase in the contact potential increases the growth rate for the first few mono layers of Nb2O5 from similar to 2.18 to similar to 2790 angstrom/s. The growth rates of oxidation on these samples become similar after the oxide thicknesses of similar to 25 angstrom are reached. We report on the basis of our studies that a protective layer should be grown in situ to avoid oxidation of Nb thin film surface of Nb/Cu cavities. (C) 2010 Elsevier B. V. All rights reserved.