Initial oxygen adsorption structures and oxidation reaction on vicinal Si͑001͒ surfaces with single-layer S A and S B steps were studied using ab initio total energy and electronic structure calculations. At the very early stage of the oxygen adsorption on Si͑001͒, the calculations in this study show that oxygen atoms are preferentially incorporated into sites at the rebonded S B step edge. Various stable oxidation structures at the rebonded S B step were identified based on total energy calculations. Their stabilities are concerned with the structural attribute of the rebonded step-edge Si atoms ͑RSAs͒ with dangling bonds and weak rebonds. In addition, the proximity of the RSAs helps form the stable oxidation structures in high oxygen coverage regions that have in common a one-dimensional ͑1D͒ -Si-O-chain structure along the step edge as a basic 1D oxide building element. By forming this 1D chain structure, it is possible to effectively reduce the number of dangling bonds ͑DBs͒ at the step edge. This indicates that the reduction of the number of step-edge DBs plays a crucial role in the formation of oxidation complexes at the steps with local strain, as seen on flat semiconducting surfaces. For more detailed information, the electronic properties of the oxidation complexes were also calculated. The calculated site-projected density of states and scanning tunneling microscopy images of the oxidation structures exhibit characteristic features distinct from those of the clean vicinal Si surface. All these results clearly show that the S B step acts as a strong sink for the oxidation of Si as suggested in experiments.