Abstarct: Density functional theory has been provided a suitable tool to study properties of wide range materials with various attributes. Using the Kohn-Sham single particle equations is one of the most important procedures to making the theory applicable . In the first and second chapters of this thesis the general properties of semiconductors , specially zinc oxide (ZnO) beiefly have been introduced . This compount is one of the favorite II–VI group semiconductor with wide band gap about 3/7 eV ( at the room temperature ) . The Doping of this semiconductor with Transition mextal (™) can be resulted to creating a new categoury of materials that are called “diluted magnetic semiconductors” (DMSs). In these chapters the applications of DMSs are also illustrated . Density functional theory and studying approach of the systems with this theory have been introduce in chapter 3. In chapter 4 WIEN2K computational code have been explaned . In chapter 5 calculation result of electronic structure and magnetic properties of TM-doped ZnO systems ( TM: Fe – Co – Mn ) have been presented.