We systematically study the electronic structure and magnetic properties of alkali metals (Li, Na, K and Rb) and alkaline earth metals (Be, Mg and Sr) doped two-dimensional GaN monolayers using the first-principles calculations based on density functional theory. The results show that Be atom is located in the plane of the GaN monolayer, and the other doped atoms reside slightly above the plane. It is found that doping is easier to achieve under the N-rich condition. The total magnetic moment of the alkali metals doped system and the alkaline earth metals doped system are 2μ_B and 1μ_B, respectively, which are presented mainly by the spin-polarized holes of the nearest N atoms of the impurity atoms. The band structures indicate that the four alkali metal atoms doped systems are magnetic semiconductors, and the three alkaline earth metal doped systems are all semi-metallic. For a double M-doped GaN monolayer system, there is a long-range ferromagnetic coupling in the seven elements doped systems, which are realized by the hole-mediated p-p hybrid interaction. The Heisenberg mean field model is used to estimate the Curie temperature. It is found that the long-range ferromagnetic coupling states of Li, Be, Mg and Sr are existent at higher than room temperature, indicating that the four atom-doped two-dimensional GaN monolayers are very good candidates for the room temperature ferromagnetic candidate materials. The alkali metals and alkaline earth metals doped two-dimensional GaN monolayers are expected to play an important role in the studying of spintronics.