This paper analyzes the influence of laser linewidth on the measurement accuracy of a frequency-scanning Brillouin optical time domain reflectometer (FS-BOTDR), allowing for both the width of Brillouin gain spectrum and the signal-to-noise ratio (SNR) of the BOTDR system. The measurement accuracy of the Brillouin frequency shift (BFS) is theoretically investigated versus the duration of the probe pulse and the linewidth of the laser source, by numerically simulating how a FS-BOTDR works and evaluating the Brillouin gain spectrum (BGS) width and the system SNR. The simulation results show that the BFS accuracy is improved as the laser linewidth becomes narrower when the probe pulse width is fixed. We utilize five types of lasers with respective linewidths of 1.05 MHz, 101 kHz, 10.2 kHz, 3.1 kHz, and 98 Hz to compare the BFS measurement accuracy over a ~10 km optical sensing fiber. The experimental results demonstrate that the root-mean-square error (RMSE) of BFS decreases with the laser linewidth narrowing from 1.05 MHz to 3.1 kHz, which is in good agreement with the numerical simulation. However, the RMSE of BFS increases when the laser linewidth is less than 3.1 kHz, which may arise from the coherent Rayleigh noise due to a too narrow laser linewidth. The results can provide a theoretical basis and experimental guidance for choosing the appropriate laser linewidth in BOTDR.