Based on first-principles, the formation energy, electronic structure and the magnetism of ZnO systems with the coexistence of Na doping and vacancy (VO or VZn) were calculated. Results show that there is the lowest formation energy when the relative distance between Na doping and vacancy(VO or VZn) is closest. Compared with the formation of VZn, Na doping is more likely to cause the occurrence of VO and excessive doping will inevitably lead to the occurrence of VO. Additionally, the magnetism of the system with the coexistence of Na doping and VZn is due to the intrinsic defect of Zn, while the electron-exchange interaction between Na doping and VO is the main reason for the magnetism of the ZnO system where Na doping and VO coexist.