The hydrogen bonding interactions of the HNO dimer have been investigated using ab initio molecular orbital and density functional theory (DFT) with the 6-311++G(2d, 2p) basis set. The natural bond orbital (NBO) analysis and atom in molecules ( AIM) theory were applied to understand the nature of the interactions. The interrelationship between one N-H center dot center dot center dot O hydrogen bond and the other N-H center dot center dot center dot O hydrogen bond has been established by performing partial optimizations. The dimer is stabilized by the N-H center dot center dot center dot O hydrogen bonding interactions, which lead to the contractions of N-H bonds as well as the characteristic blue-shifts of the stretching vibrational frequencies v( N- H). The NBO analysis shows that both rehybridization and electron density redistribution contribute to the large blue-shifts of the N- H stretching frequencies. A quantitative correlations of the intermolecular distance H center dot center dot center dot O (r(H center dot center dot center dot O)) with the parameters: F at bond critical points (BCPs), s-characters of N atoms in N- H bonds, electron densities in the sigma*( N- H), the blue-shift degrees of v(N-H) are presented. The relationship between the difference of rho (vertical bar Delta rho vertical bar) for the one hydrogen bond compared with the other one and the difference of interaction energy (Delta E) are also illustrated. It indicates that for r(H center dot center dot center dot O) ranging from 2.05 to 2.3528 angstrom, with increasing r(H center dot center dot center dot O), there is the descending tendency for one rho(H center dot center dot center dot O) and the ascending tendency for the other rho(H center dot center dot center dot O). r(H center dot center dot center dot O) ranging from 2.3528 to 2.85 angstrom, there are descending tendencies for the two F(H center dot center dot center dot O) with increasing r(H center dot center dot center dot O). On the potential energy surface of the dimer, the smaller the difference between one F(H center dot center dot center dot O) and the other F(H center dot center dot center dot O) is, the more stable the structure is. As r(H center dot center dot center dot O) increases, the blue-shift degrees of v(N-H) decrease. The cooperative descending tendencies in s-characters of two N atoms with increasing r(H center dot center dot center dot O) contribute to the decreases in blue-shift degrees of v(N-H). Ranging from 2.05 to 2.55 angstrom, the increase of the electron density in one sigma*(N-H) with elongating r( H,,, O) weakens the blue-shift degrees of v( N- H), simultaneously, the decrease of the electron density in the other sigma*(N-H) with elongating r(H center dot center dot center dot O) strengthens the blue-shift degrees of v( N- H). Ranging from 2.55 to 2.85 angstrom, the cooperative ascending tendencies of the electron densities in two sigma*(N-H) with increasing r(H center dot center dot center dot O) contribute to the decreases in blue-shift degrees of v(N-H).