The molecular structure of a new Schiff base, 2-[4-hydroxy benzylidene]-amino naphthalene (HBAN) has been examined by HF and B3LYP/6-311++G(d,p) calculations. The X-ray structure was determined in order to establish the conformation of the molecule. The compound, C17H13NO, crystallizes in the orthorhombic, P212121 space group with the cell dimension, a=6.2867(2), b=10.2108(3), c=19.2950(6) Å, α=β=γ=90° and z=4. The asymmetric unit contains a molecule of a Schiff base. A strong intermolecular O-H⋯N and a weak C-H⋯O hydrogen bonds stabilized the crystal structure. The vibrational spectra of HBAN have been calculated using density functional theoretical computation and compared with the experimental. The study is extended to the HOMO-LUMO analysis to calculate the energy gap (Δ), Ionization potential (I), Electron Affinity (A), Global Hardness (η), Chemical Potential (μ) and Global Electrophilicity (w). The calculated HOMO and LUMO energy reveals that the charge transfer occurs within the molecule.