The mechanical properties of cells and tissues play a crucial role in determining biological functions. As a label-free and non-contact mechanical imaging method, Brillouin spectroscopy can characterize viscoelastic changes in samples with high spatial resolution. To sensitively identify small mechanical differences among biological systems, it is important to improve Brillouin scattering efficiency while combining various viscoelastic contrast mechanisms in measurement. This paper presents a high-speed Brillouin spectroscopy based on impulsive stimulated Brillouin scattering. The acoustic oscillation can be excited in a single shot with a pulsed pump laser and detected by a continuous probe laser in the time domain. This time-domain signal can then be transferred to the frequency-domain Brillouin spectrum with high precision. With this method, various viscoelastic information including sound velocity, sound attenuation coefficient, elastic longitudinal storage modulus, and loss modulus can be obtained simultaneously based on derived spectral information. Owing to stimulated scattering and time-domain detection, spectra with a signal-to-noise ratio of 26 dB can be achieved within a millisecond-level spectral integration time. The average measurement precision for storage modulus and loss modulus of the longitudinal elastic modulus are 0.1% and 1%, respectively. With this method, the Brillouin spectra and viscoelastic parameters of typical liquids and polymer materials are measured and compared, providing a comprehensive reference for viscoelastic parameters. We also study the elastic changes in different curing stages of PDMS and make a comparison of viscoelasticity with agarose gel. Moreover, six edible oils are identified based on various viscoelastic contrast mechanisms, which not only provides a new perspective for material identification but also expands the measurement capabilities of Brillouin spectroscopy and enhances the sensitivity of viscoelasticity measurements.