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The theoretical study of PuOn＋(n＝l,2,3) using a density functional method shows that PuO＋ (X6∑-) and PuO2＋ (X5∑-, 7∑-, 9∑-) ions are stable, and the PuO3＋ (4∑＋, 6∑＋) ion is unstable. The analytic potential energy functions of X6∑- for PuO＋ and X5∑-, 7∑-, 9∑- for PuO2＋ have been derived, and their force constants and spectroscopic data have been calculated.