For the first time, to the best of our knowledge, a direct detection Brillouin optical time-domain reflectometry (BOTDR) is demonstrated for fast distributed dynamic strain sensing incorporating double-edge technique, time-division multiplexing technique and upconversion technique. In order to guarantee the robust stability of the system, the double-edge technique is implemented by using a convert single-channel FPI and a fiber-coupled upconversion single-photon detector, incorporating a time-division multiplexing method. The upconversion single-photon detector is adopted to upconvert the backscattering photons from 1548.1 nm to 863 nm, which is subsequently detected by a Silicon avalanche photodiode (Si-APD). In the experiment, dynamic strain disturbance up to 1.9 mε over 1.5 km of a polarization maintaining fiber is detected at a sampling rate of 30 Hz. An accuracy of and spatial resolution of 0.6 m are realized.