A distributed dynamic strain measurement is demonstrated using small gain stimulated Brillouin scattering (SBS) in Brillouin optical time domain reflectometry based on the short-time Fourier transform algorithm. The input power limits, frequency uncertainties for given pulse durations, fiber lengths, and the number of averaging are calculated. The output signal power and the signal-to-noise ratio of the system output are enhanced by SBS. It is found that the signal processing is faster and requires fewer averaging to achieve dynamic sensing performance along the fiber under test. A 60-Hz vibration on a 6-m fiber section at the end of a 935-m fiber is detected with the spatial resolution of 4 m with a sampling rate of 2.5 kS/s.