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Ferromagnetism of ZnO-based magnetic semiconductors was investigated by ab initio calculations based on the local density approximation. In a system of Mn atom doped ZnO, the ferromagnetic ordering of Mn magnetic moments was induced by hole doping. It was also found that 3d transition metal atoms of V, Cr, Fe, Co and Ni showed the ferromagnetic ordering of their magnetic moments in ZnO without any additional carrier doping treatments. Appearance of the ferromagnetism in these systems suggests possibility for a fabrication of a transparent ferromagnet which will have great impact on industrial applications in magneto optical devices.