Brillouin optical correlation-domain reflectometry (BOCDR) is known as one of the distributed fiber-optic strain/temperature sensing techniques. Recently, a high-speed BOCDR configuration with no measurable strain limit has been developed, but only a sampling rate of 50 Hz has been experimentally demonstrated, limited by the use of a commercial microwave frequency sweeper (MFS). In this work, by replacing the MFS with an independent voltage-controlled oscillator driven by a function generator, we experimentally show via vibration detection that this system can achieve a sampling rate of up to 20 kHz. We newly observe the systematic noise peculiar to such high-speed operation, which is found to originate from the unintended intensity modulation of the laser output. We also demonstrate the suppression of this noise by band-elimination filtering.