The potential energy functions and spectrum constants of VOn±(n=0,1,2) have been analyzed by the density functional method (B3LYP/6-311++G(d, p) and using the relativistic effective core potential (Lanl2dz). The results show that all of them can exist stably. Their ground electronic states are 4Σ (VO2-), 3Σ (VO-), 4Σ(VO), 3Σ(VO+) and 2Σ(VO2+). Among them, the potential energy curves of VO2+ and VO2- have the form of a volcanic crater. The molecules of VO2+ and VO2- are in meta-stable states. The potential energy curves of VO2+ and VO2- have been fitted with the seven-parameter Murell-Sorbie functions. It has been found that the fitting cures of the meta-stable ions VO2+ and VO2- are well in accordance with their potential energy curves. However, the four-parameter Murell-Sorbie functions are not suitable for VO2+ and VO2-. At the same time, the effect of charge on the potential energy functions and energy levels have been discussed.