Stress corrosion cracking (SCC) of stainless steels used in light water reactor nuclear power plants is a potentially critical issue concerning safety of plant operation. Chemical reactions of steel surfaces in high temperature water such as oxidation and/or anodic dissolution, and subsequent formation of protective film is a crucial process in crack propagation of SCC, and therefore, it is important to understand the interaction of water with iron based alloys for understanding SCC mechanisms. In this study, in order to obtain better knowledge of the surface chemistry of iron based alloys in the presence of high temperature water, we performed a tight-binding quantum molecular dynamics calculation of the initial oxidation stage of pure Fe and Fe-Cr alloy surfaces. H2O molecules were dissociated on the Fe and Fe-Cr surfaces at 561 K. Chromium atoms at the top layer segregated from the surfaces faster than iron atoms to bond with oxygen atoms. Chromium concentration around the oxygen gradually increased to form Cr-O bonds, which resulted in clustering of oxygen and chromium atoms. The clustering of oxygen and chromium is believed to bring about Cr-based oxide nucleation and therefore, the formation of Cr-O bonds is considered to be the initial process of the formation of oxide films on the Fe-Cr alloy surface.