In order to enrich the potential of gallium nitride (GaN) monolayer in low-dimensional spintronic devices, we implement a theoretical study of the magnetic properties of group VIII B transition-metal (TM)-substituted GaN monolayer (ML). The results show that the group VIII B TM atom-substituted systems exhibit a distinct nonzero magnetic moment. The total magnetic moment of the Fe- and Ru-substituted systems is 5 mu(B), while that of Co- and Rh-substituted systems is 4 mu(B). Asymmetry of the degenerate and nondegenerate states, based on whether, and how, they are occupied, or not occupied by electrons in spin-up and spin-down bands decides the magnetic moment. The origin of magnetic moment is polarization of TM 3d or 4d electrons and N 2p electrons. Furthermore, co-doping of different TM atoms can increase the magnetic moment of GaN ML.