We propose a multi-element hopping model, which shows the flux equations of various cations under high electric field. The model is applied to the initial oxidation of binary alloys which produces a homogeneous single layer solid solution oxide film. The flux equations by this model for two kinds of cations were substituted to the oxidation growth rate definition equation. Finally, it is shown that the initial oxidation rate law of dilute binary alloys can be obtained as a type of inverse logarithmic rate law.