We have developed a high precision stimulated Brillouin spectrometer. Since this spectrometer is based on the stimulated light scattering, Brillouin measurements are possible without any signal reduction even at extremely low temperatures. The use of stable lasers for the pump and probe waves and a real-time frequency-monitor gives a high frequency resolution reaching 20 kHz, which is, to the best of authors knowledge, the highest resolution so far reported for Brillouin spectrometers. The frequency-monitor has been achieved through the measurement of the beat frequency between the two lasers by using a microwave frequency counter. With this spectrometer, we have succeeded to measure Brillouin spectra in single crystals of TeO2 from room temperature to liquid helium temperature. Furthermore, in a sample with  surfaces, we have observed a spectral splitting due to the multireflection of phonons at crystal surfaces.