We analyzed the current-voltage (I-V) characteristics of ultrathin SiO2/Si(111) and its relation with the surface step density. The oxides were grown on flat (0 degrees-off) and vicinal (0.5 degrees-off) substrates in dry O-2 with variation of oxidation temperature and thickness, from 500-800 degrees C and from 1.5-2.0 nm, respectively. The I-V curves indicated that the steps were preferable sites for the formation of interface states, when the oxides were grown at around 600 degrees C. However, the correlation between the current and step density became smaller when the oxides were grown at lower or higher temperatures. We also found that the correlation was reduced as oxidation proceeded and the oxides became thicker. A model to explain the results was suggested by taking into account of the relaxation of oxide films around the steps and on terraces.