A new phase-coherent Rayleigh--Brillouin scattering method using frequency-tunable cw lasers has been developed. Spontaneous Brillouin scattering is caused by thermally excited phonons whose phases have no physical meaning because of their random, incoherent nature. Thus only the power spectrum of the density fluctuations is measurable. In principle, however, coherent phonons having phase information can be generated by a scanning interference pattern that is produced by intersecting two laser beams with slightly different frequencies. When the dispersion relation of the phonon is satisfied, coherent phonons are generated resonantly in a sample. This resonance spectrum is physically equivalent to the spontaneous Brillouin spectrum. By a phase-sensitive heterodyne detection of the scattered light due to light-induced coherent phonons, complex Brillouin spectra have been measured for the first time. Since frequency-tunable cw lasers with high phase coherency are used, this method has a high-frequency resolution of ~1 MHz, irrespective of the phonon frequency. The method has an extremely high sensitivity because of the coherent detection of signals while keeping a much higher frequency resolution than a Fabry--Perot interferometer. It is hoped that the method will be applied for studying the dynamics of acoustic phonons in various condensed matter, superseding a Fabry--Perot interferometer.