Using first-principles calculations, we explored all the 21 defect-pairs in GaN and considered 6 configurations with different defect-defect distances for each defect-pair. 15 defect-pairs with short defect–defect distances are found to be stable during structural relaxation, so they can exist in the GaN lattice once formed during the irradiation of high-energy particles. 9 defect-pairs have formation energies lower than 10 eV in the neutral state. The vacancy-pair V_N–V_N is found to have very low formation energies, as low as 0 eV in p-type and Ga-rich GaN, and act as efficient donors producing two deep donor levels, which can limit the p-type doping and minority carrier lifetime in GaN. V_N–V_N has been overlooked in the previous study of defects in GaN. Most of these defect-pairs act as donors and produce a large number of defect levels in the band gap. Their formation energies and concentrations are sensitive to the chemical potentials of Ga and N, so their influences on the electrical and optical properties of Ga-rich and N-rich GaN after irradiation should differ significantly. These results about the defect-pairs provide fundamental data for understanding the radiation damage mechanism in GaN and simulating the defect formation and diffusion behavior under irradiation.