The magnetic properties of carbon doping GaN have been examined in combination of first-principles density functional calculations and experiments. The calculated results indicate that a single C dopant produces a spin magnetic moment of about 0.7 mu(B) and the two-C-atoms form a stable ferromagnetic coupling when their distance lies around 5-6 angstrom, which can be explained by the C2p magnetic orbitals overlapping via the nearest Ga p-d orbitals and next-nearest N2p orbitals. The ferromagnetism is also observed in our C-doped GaN samples with high C/Ga ratio. (C) 2010 Elsevier B.V. All rights reserved.