We have investigated the electronic structure and magnetism of anion doped GdN_1−yX_y (X = B, C, O, F, P, S and As) systems by first-principles calculations based on density functional theory. GdN_1−yX_y systems doped by O, C, F, P, and S atoms are more stable than those doped by B and As atoms because of relatively high binding energies. The anion doping and the N defect states modify the density of states at the Fermi level, resulting in a decrease in spin polarization and a slight increase in the magnetic moment at the Gd and N sites.