Abstract: Electronic structure and magnetic moments of (Boron) B-doped ZnO was investigated by ab initio electronic structure calculations based on the density functional theory (DFT) with the generalized gradient approximation (GGA). We also performed GGA+U calculations to further refine our results. It is found that single B atom at O site in ZnO becomes spin polarized with its many neighboring atoms with a total magnetic moment of 0.94 and 1.27 μB for GGA and GGA+U respectively. The magnetic coupling between doped B atoms is substantial leading to either antiferromagnetism or ferromagnetism with GGA+U. For the B-B distance is 7.942 Å by replacing two oxygen atoms at the opposite vertices of a ZnO wutizte. A strong antiferromagnetic coupling occurs.