Frequency scanning is a common method of BOTDR demodulation Brillouin gain spectrum (BGS). In the frequency scanning process, the electrical band-pass filter is important, and the bandwidth of the electrical filter has an effect on the performance of BOTDR. This paper focuses on the influence of band-pass filter (BPF) bandwidth on the measurement spectral width of BGS and spatial resolution of the frequency-scanning Brillouin optical time domain reflectometer (FSBOTDR), which further affects the measuring performance of BOTDR. The law of BFS accuracy and spatial resolution (SR) with filter bandwidth is theoretically investigated by analyzing the work principle of FS-BOTDR in numerical and evaluating the Brillouin gain spectrum width. Five filters with bandwidths of 40MHz, 55MHz, 70MHz, 85MHz, 100MHz in 700MHz center frequency is selected to compare the spatial resolution and BFS accuracy, which depend on the BGS spectral width. The analyzing and experimental results show that the spatial resolution improves with increasing the filtering bandwidth. When filter bandwidth increases, the BGS spectral width could be broadened, means the sensitivity of the filter output power to the frequency shift is decreased, which caused the reducing of measurement accuracy. The research can be a theoretical basis and experimental guidance on the choosing of filter bandwidth for FSBOTDR.