Fabrication of good Ohmic contacts is quite important not only for device application but also for fundamental physics. In accordance with the device scaling, it is inevitable to prepare nano-scale Ohmic contacts for future LSIs technology. In this study, we hereby propose a new electronic structure model for Ohmic contacts, with which it is possible to describe the real situation precisely. Our proposed model contains many discrete levels that originate from vacancies and impurities located in the vicinity of the metal and the semiconductor interface, within the energy range of the Schottky barrier height. We calculate the current-voltage characteristics based on our proposed model. Calculated results show that our proposed model reveals linear Ohmic I-V characteristics without conventional band alignment for the Ohmic contacts. Moreover, we found that energy distribution of the discrete levels is important for obtaining Ohmic characteristics.