Wide band gap Oxide based diluted magnetic semiconductors (ODMS) exhibit unique magnetic, magneto-optical and magneto-electrical effects and can be exploited as spintronic devices. Theoretical studies of transition metal (TM) doped zinc oxide which belongs to these class of materials has been attracting significant research interest in the recent years. In this paper, the electronic band structures, and band gap energies of ZnO doped with transition metal have been analyzed by ab initio calculations based on the density functional theory using quantum espresso PWscf code. For the band gap calculations, we have used both local density approximation (LDA) and generalized gradient approximation (GGA). The magnetic and optical properties of the materials have been studied using the above method. For all the theoretical calculations, the model structures of transition metal-doped ZnO were constructed by using the 16 atom supercell with one Zn atom replaced by a transition metal atom. The results are useful in understanding the band gap variations with doping and other related properties in oxide based diluted magnetic semiconductors such as ZnO.