A series of Mn-doped ZnO films have been prepared in different sputtering plasmas by using the inductively coupled plasma enhanced physical vapour deposition. The films show paramagnetic behaviour when they axe deposited in an argon plasma. The Hall measurement indicates that ferromagnetism cannot be realized by increasing the electron concentration. However, the room-temperature ferromagnetism is obtained when the films are deposited in a mixed argon-nitrogen plasma. The first-principles calculations reveal that antiferromagnetic ordering is favoured in the case of the substitution of Mn2+ for Zn2+ without additional acceptor doping. The substitution of N for O (NO-) is necessary to induce ferromagnetic couplings in the Zn-Mn-O system. The hybridization between N 2p and Mn 3d provides an empty orbit around the Fermi level. The hopping of Mn 3d electrons through the empty orbit can induce the ferromagnetic coupling. The ferromagnetism in the N-doped Zn-Mn-O system possibly originates from the charge transfer between Mn2+ and Mn3+ via NO-. The key factor is the empty orbit provided by substituting N for O, rather than the conductivity type or the carrier concentration.