[en] The d"0 ferromagnetism in wurtzite GaN is investigated by the first-principle calculations. It is found that spontaneous magnetization occurs if sufficient holes are injected in GaN. Both Ga vacancy and Na doping can introduce holes into GaN. However, Ga vacancy has a high formation energy, and is thus unlikely to occur in a significant concentration. In contrast, Na doping has relatively low formation energy. Under N-rich growth condition, Na doping with a sufficient concentration can be achieved, which can induce half-metallic ferromagnetism in GaN. Moreover, the estimated Curie temperature of Na-doped GaN is well above the room temperature. - Highlights: • Hole-induced ferromagnetism in GaN is confirmed. • Both Ga Vacancy and Na-doping can introduce hole into GaN. • The concentration of Ga vacancy is too low to induce detectable ferromagnetism. • Na-doped GaN is a possible ferromagnet with a high curie-temperature.