Wavelength dependent hyper-Rayleigh scattering measurements have been performed by using a fluorescence spectrometer. With this detection strategy, first molecular hyperpolarizability (β) of a dual charge-transfer (H-shaped) chromophore and its monomer have been measured in two-photon resonance range from 670 to 950 nm as well as at off-resonance of 1064 nm. The absorption and resonance hyper-Rayleigh profiles can be simulated reasonably well with a common set of parameters. In addition, both resonance and off-resonance results show that β(0) per chromophore has a remarkable enhancement for the H-shaped molecule as large as 1.7, compared with that of the monomer, which could be ascribed to two physical effects: (1) coherent enhancement of two chromophores and (2) intramolecular dipole-dipole interaction, which was confirmed by their fluorescence-decay behaviors.