Lithium overstoichiometric LixCoO2 (x > 1) with few phase transitions is promising as a positive electrode material for lithium ion batteries; however, the detailed lithium local structures around excess Li ions remain unknown and need to be elucidated. It has been postulated that the excess Li ion occupies the Co site, and the resulting charge deficit is compensated for by oxygen vacancies and the valence of Co. Two spin states have been invoked for the Co ion; one is Co3+ taking an intermediate spin state (S = 1) and the other is low spin Co2+ (S = 1/2). The paramagnetic shift caused by the Co spin is appreciable by Li-6/7 nuclear magnetic resonance (NMR) in solids using magic-angle spinning (MAS), and we show that there are five "major" minor signals at ca. -16, -6, 3, 185, and 1100 ppm with the intensity ratio of 2:4:4:2:0.5-1.0, in addition to the major signal at 0 ppm. Analysis of temperature-dependent Li-7 shifts and also Li-6 T-1 experiments confirm that the observed shifts for these minor peaks are ascribed to the paramagnetic interaction. To examine distance proximities among these lithium ions at the minor sites, we apply three Li-7-Li-7 two-dimensional (2D) correlation experiments and show that the three minor lithium atoms, whose shifts are 3, 6, and 16 ppm, exist in the same Li layer. Further, from rotational-resonance recoupling experiment, it is indicated that the lithium appearing at -16 ppm is closest to that at ca. 185 ppm. Based on these results, we show that a defect structure assuming low spin Co2+ which is not associated with the oxygen vacancy is consistent with the NMR results. This leads us to invoke Li insertion at an interstitial site, which has been negated, for the position of the excess Li atom.