The Fe-Ni Invar alloy is often employed under extreme conditions such as high temperatures, high pressures, and corrosive environments, making it susceptible to oxidation and subsequent failure. Hence, a thorough understanding of its oxidation behavior is crucial. We performed ReaxFF-based molecular dynamics (MD) simulations to study the oxidation behaviour of Fe-Ni Invar alloy at the atomic scale under extreme conditions. The initial stage of oxidation involves the preferential adsorption and dissociation of O2, demonstrating its surface-site selectivity. The initial oxidation kinetics follows a logarithmic law, and the whole oxidation process results in dominant low-coordinated clusters configurations in the oxide film. Simultaneously, Fe atoms tend to donate more electrons to O atoms than Ni atoms. Moreover, the O2 consumption rate were found to increase with pressure and amorphous oxides formed more readily under high pressure. Our results indicate that adjusting the pressure may enhance the oxidation resistance of the Fe-Ni alloy, which is significant for the design and application of alloys in extreme conditions.