We report in situ atomic-resolution transmission electron microscopy observations of the oxidation of stepped Cu surfaces. We find that the presence of surface steps both inhibits oxide film growth and leads to the oxide decomposition, thereby resulting in oscillatory oxide film growth. Using atomistic simulations, we show that the oscillatory oxide film growth is induced by oxygen adsorption on the lower terrace along the step edge, which destabilizes the oxide film formed on the upper terrace.