We have developed a new method of Rayleigh-Brillouin spectroscopy, which we call "Phase-Coherent Rayleigh-Brillouin Scattering" method. In our method, we optically generate acoustic phonon by crossing two frequencytunable cw laser beams in a sample. Since the phase of the phonon is coherent to those of the light waves, we can observe complex RayleighBrillouin spectra that cannot be obtained by any methods measuring spontaneous fluctuations. We succeeded in observing the complex Brillouin spectra of carbon disulfide with the phonon frequency at 7.6GHz. This is the highest phonon frequency measured by optical-beating technique using cw lasers, to our knowledge. We applied our method to the study of Rayleigh spectra of thermal diffusion mode in a critical solution of methanol and cyclohexane, and succeeded in measuring the complex Rayleigh spectra of thermal diffusion mode selectively. Even under the strong concentration fluctuations near a critical point, our method enables us by generating phase-coherent temperature gradient to observe Rayleigh spectra of thermal diffusion mode selectively.