The electronic and magnetic properties of Cu-doped GaN with a Cu concentration of 6.25% and 12.5% are examined theoretically using the full-potential linear muffin-tin orbital method. The magnetic moment of Cu atoms decreases with increasing Cu concentration. The spin-polarization of Cu atoms is reduced due to the Cu d-d interaction depending on the distance between the nearest neighbouring Cu atoms. Cu atoms exhibits a clustering tendency in GaN. For Cu-adsorbed GaN thin films with a surface coverage of 0.25, the ferromagnetic state is found to be the energetically favourable state with an induced magnetic moment of $0.54;{mu}_B$ per supercell.