In order to investigate the electronic and magnetic properties of Co-ZnO alloys, we used a full-augmented-plane-wave (FPLAPW) method within the density functional theory (DFT), as implement in the WIEN2K package. This work is carried out within the LSDA approximation as the exchange-correlation potential. We have modelled ZnO doped with 6.25%, 12.5%, and 18.75% of Co. It pointed out that the band gap and the magnstic moments increase with the atomic fraction of Cobalt. The ZnxCo1-xO is found to be a semiconductor, where the filled-states are located in the valence bands and the empty ones above the conduction dand edge. The filled and empty d-states are also shown to shoft downwards and upwards in the valence and the conduction bands, respectevly, with increase in the U potential. The total density of states (TDOS) and local density of states (LDOS) of the d electrons shed light on the evolution of the elctronic properties.