We have done the spectral investigations of protonated naphthalene (NpH+) theoretically. The optimized molecular geometry, structural parameters, harmonic frequencies, atomic charges, dipole moment and several thermodynamic functions of protonated naphthalene (NpH+) have been calculated using the Becke three-parameter Lee-Yang-Parr functional (B3LYP) and 6-311++G(d,p) basis set. The calculated vibrational wave numbers of protonated naphthalene have been systematically analyzed and assigned to different normal modes of the molecules.