The central theme of nanotechnology to miniaturize devices has stimulated interest in diluted magnetic semiconductors (DMS). DMS that simultaneously exhibit magnetic and semiconducting behavior are capable of parting properties of two different function devices into one. In this research we present our first principles investigations related to the structural and electronic properties of, Cr doped zinc-blende (zB) ZnO, DMS. These calculations are carried out using full potential linearized augmented plane wave plus local orbital (FP-L(APW+lo)) with generalized gradient approximations approach as implemented in WIEN2k code. In this study, the effect of Cr doping on lattice parameters, spin polarized electronic band structure, density of states (Dos) of ZnO is presented and analyzed in detail.