The first hyperpolarizability (beta) of a strongly charge-transfer (azulenic-barbituric) chromophore is measured by hyper-Rayleigh scattering (HRS) experiment using 11 excitation wavelengths, ranging from 900 nm to 1907 nm. The measured wavelength-dependence of the beta value is used to investigate the dispersion relation of the first hyperpolarizability of the charge-transfer chromophore. When excited by the 1064 nm wavelength laser radiation, the experimental HRS spectrum shows a two-photon resonance (TPR) peak, which does not coincide with the maximum of the linear absorption spectrum. The wavelength dependence of the first hyperpolarizability cannot be explained by an undamped or damped two level model. However, incorporating vibrational motion in the damped two-level model results in a good fit between theoretical and experimentally measured beta, especially in the vicinity of TPR region.