Brillouin spectroscopy allows non-invasive measurement of the mechanical properties of a sample by measuring the spectra of acoustically induced light scattering therein, and thus has been widely investigated for biomedical application. Recently, the development of fast Brillouin spectrometry based on virtually-imaged phased array (VIPA) has made in-situ measurement of biomedical sample possible. However, one limitation of current Brillouin technique is the low spectral extinction, which limits the measurement to nearly transparent sample. In order to measure turbid sample, multistage VIPA can be cascaded to gain spectral extinction. For example, spectral extinction of ~80 dB was achieved using three-stage VIPA; however, this approach significantly sacrificed measurement throughput. In this work, we develop a novel spectrometer that achieves high extinction without significant signal loss. To achieve this goal, we combine a two-stage VIPA spectrometer with a triple-pass Fabry-Perot interferometer. The triple-pass Fabry-Perot interferometer acts as a band-pass filter with ~3 GHz bandwidth and ~35-dB spectral extinction. Therefore, the overall extinction of this spectrometer greatly surpasses 80 dB with only ~20% excess loss. We demonstrated the performance of this spectrometer measuring background-free Brillouin spectra from Intralipid solutions and within chicken tissue.