PACS 75.50. Pp, 81.05.Ea, 81.15.Hi c-axis-oriented Cr-doped hexagonal GaN films with Cr of 0.3, 1 and 5 at.% were epitaxially grown on GaAs(111)A substrates by metal organic molecular beam epitaxy (MOMBE) with metal Ga and dimethylhydrazine (DMHy) as a nitrogen source. Clear hysteresis loop was observed in magnetization versus magnetic filed (M -H) curves for Cr-doped GaN films, and the ferromagnetic behaviour was confirmed even at 350 K. The saturation magnetization per Cr atom is estimated to be approximately 1 Bohr magnetron at 300 K.