Abstract: Experimental measurement of the three-dimensional momentum of the recoil ion He⁺ produced by single-electron capture of 0.64 keV/u N⁺ with He using the reaction microscopy imaging spectrometer with a two-fold coincident method, and the state-selective cross-sections and angular distributions of an electron captured into different quantum states of the projectile ions have been obtained. The experimental results show that the ground state projectile N⁺(³P) captures a 1s electron from the He target mainly to the 2p shell, and the contribution to the higher shells can also be observed; the metastable N⁺(⁵S) captures a 1s electron from the He target mainly to the 2s shell, with almost no contribution to higher shells. The experimental results are interpreted qualitatively using the potential energy curves of the NHe⁺ quasimolecular ion, but the reaction window predictions of the molecular Coulomb over-barrier model differ significantly from the experiments. During the capture of the target electron into the 2s orbital by the metastable projectile N⁺(⁵S), a clear oscillatory structure appears in the angular differential cross-section, which is likely to result from Demkov-type transitions.