We demonstrate a one-end-access high-speed distributed strain sensing with high spatial resolution in optical fibers based on Brillouin optical correlation-domain reflectometry. In this work, Brillouin frequency shifts (BFSs) of a 3- cm fiber section are measured with 13- mm spatial resolution and 50- Hz sampling rate. To our knowledge, this spatial resolution is the best result ever reported in Brillouin scattering-based reflectometers, and is superior to that obtained in Brillouin optical time-domain analyzers, though the signal-to-noise ratio is deteriorated. Data processing to find the peak in the Brillouin spectrum is newly introduced to show directly the BFS with a sampling rate of 19 Hz, and the measurement of vibrated strains at frequencies of up to 4 Hz is presented under 22- cm resolution.