By using first principles, the p-doping mechanism of two-dimensional GaN with buckled structure is discussed in detail under various doping configurations, including different doping elements, positions, and concentrations. The research implies that difference in electronegativity between three doping elements: Be, Zn, Mg and two-dimensional GaN results in a significant change in atomic structure and charge distribution. When Be, Zn, and Mg atoms are doped at Ga position, doping process in two-dimensional GaN is easier because their formation energies are 1.684, 4.630, and 3.390 eV, respectively, which are lower than doped at N position. In addition, Ga doping site is more favorable for p-type doping because bandgap and work function of two-dimensional GaN are reduced and it would convert into p-type semiconductor when a Ga atom is replaced by dopants.