Abstract: We report the results of a theoretical study of magnetic coupling between Cr atoms doped in cubic GaN.The calculations are within the framework of density functional theory.By varying the concentration of doped Cr atoms and the sites they occupy,the electronic structure and magnetic properties of Cr-doped cubic GaN are calculated.It is found that the ferromagnetic phase of Ga_1-xCr_xN is energetically the most preferable state irrespective of the concentration and site occupation of the Cr atom.Cr atoms cluster around N and couple ferromagnetically,while the neighboring N atom is antiferromagnetically coupled to the Cr spin in the zinc blende Ga_1-xCr_xN.The origin of the ferromagnetism in the Cr-doped cubic GaN can be understood by double-exchange mechanism.The calculated results are consistent with the recent experimental discovery of ferromagnetism in Cr-doped GaN single cubic phase.