First principle calculation, based on density functional theory, is applied to study the configuration and electronic structure of ZnO screw dislocations along [0001] and [112¯0]. O-O bonds can be found in the core of dislocations along [0001], which induces an occupied energy level in forbidden band. The dislocations along [0001] also facilitate the formation and accumulation of Zn vacancies, due to the stress relief in dislocations. Moreover, the dislocations are periodic and continuous, and can mediate the ferromagnetic coupling between Zn vacancies. The antibonding state of O-O bonds around Zn vacancies is responsible for the ferromagnetic state, which is a kind of d0 ferromagnetism. The result also gives us a new view to think the origin of d0 ferromagnetism in ZnO.