The effects of vacant, O defects and As doping on the structures and properties of Ge nanocrystals (Ge-ncs) are investigated by using first-principles calculation based on the density functional theory (DFT). The calculation results indicate that the O defects induced by thermal annealing cannot compensate for the defects caused by neutron irradiation in Ge nanocrystals, while the introduction of As produced by neutron transmutation doping (NTD) will do the jop. We also show that the strong attraction between O and Ge atoms inhibits the formation of vacant defects in Ge nanocrystals, and further improve the luminescent property of Ge-SiO2 system. This suggests that it is necessary to perform thermal annealing for Ge-ncs structures before NTD. Our calculations well support our previous experimental results.