In this work, we investigate systematically single-electron capture process in N⁶⁺(1s) ion and H(1s) atom collisions in a wide energy domain ranging from 0.25 to 225 keV/u using a two-electron semiclassical asymptotic-state close-coupling approach. Spin-averaged and spin-resolved total cross sections, along with n-resolved and nℓ-resolved partial cross sections, are calculated and comprehensively compared with existing experimental measurements and theoretical predictions. The results show a weak energy dependence of total cross sections at low energies (<10 keV/u), followed by a monotonic decreasing trend at higher energies. The analysis of nℓ- resolved cross sections reveals the strong coupling effects between various channels in low energies, while at high energies the relative ℓ distributions in each nℓ-resolved cross sections approximately follow the statistical ℓ distribution, for which the electron is therefore mainly captured into subshells of the maximum ℓ. The present study demonstrates the importance of a two-electron treatment taking into account electronic correlation and the use of extended basis sets within the close-coupling scheme. However, substantial discrepancies exist among theoretical approaches at low energies, it is clear that further experimental and theoretical efforts are required to draw definite conclusions. Our work provides a complete and consistent set of cross sections over a broad range of collision energies, which can be used for various plasma diagnosis and modeling. All the data presented in this paper are openly available at https://www.scidb.cn/s/3a6Vji .