The total energies and electronic structures of differently configured Nb2H are calculated using pseudopotential plane wave method based on density functional theory and generalized gradient approximation. The results show that hydrogen atom favors tetrahedral (T) sites (T-wells) rather than octahedral (O) ones. There exist lower energy paths along adjacent T-T sites and saddle structures at the midpoint of them. When H is at T-site or along the T-T path, its 1s level is less broadened and the 4d, 5s bands of Nb extend downward from the metallic band area, forming an ionic band (sharp peak) separated by a gap of about 1 eV from the metallic valence bands, showing that the hydrogen atom captures one valence electron to form an anion. This low-lying ionic band loses its T-site hybridization features when H moves from T to O site, where the 1s band of H is widely broadened, extending into the metallic valence bands. The band structure changes only slightly when the hydrogen atom moves from one T site to a neighbor one along the lower energy path, keeping the T-configuration features. The calculated phonon spectra of H are dispersive only near special q-points for the system with H at a T site, showing that the hydrogen atom is probably vibraing locally and weakly interacts with other hydrogen atoms. The behavior of H at a trapping site plays an important role in bonding of the surrounding Nb atoms.