Abstarct: In this research, the strength of intramolecular hydrogen bonding of 1,5-dihydroxyanthraquinone (1,5DHA) was investigated by means of density functional theory (DFT) calculations, the quantum theory of atoms in molecules (AIM), and the natural bond orbital (NBO) analysis. 1,5DHA was optimized and the vibrational frequencies were calculated at the B3LYP/6-311++G** level of theory. The results of molecular structure, the frequencies of OH bond, the chemical shifts of enolic proton, and the topology of 1,5DHA in the bond critical point of O··H were compared with the analogous parameters of 1,8-dihydroxyanthraquinone (1,8DHA) 2-hydroxybenzaldehyde (2HB) and 1-hydroxyanthracen-9(10H)-one (1HA). The nonlinear optical (NLO) property, dipole moment, polarizability, hyperpolarizability and frontier molecular orbital surfaces (FMOs) of 1,5DHA were also calculated. From AIM result, the interaction of intramolecular hydrogen bonding of these compounds is partially covalent in nature and these compounds are classified as the systems with medium hydrogen bonds. Comparison of the molecular structure, vibrational spectra and AIM results of 1,5DHA with those of 1,8DHA, 2HB, and 1HA revealed the following trend in the hydrogen bond strength: 1HA> 1,5DHA> 1,8DHA> 2HB. The parameters related to NLO property showed that 1,5DHA is not a good NLO material but 1,8DHA and 2HB are good ones. FMOs analysis indicated that the softness decreases in 1,5DHA, 1,8DHA, 1HA and 2HB, respectively. The small HOMO–LUMO energy gap for the tixtle compounds indicates that these molecules are very chemical reactive.