We propose a scheme using the frequency-agile technique to measure Brillouin gain and loss spectra simultaneously to simplify the experimental equipment and improve the signal-to-noise ratio (SNR) of the traditional Brillouin optical time-domain analysis (BOTDA) system. The pump wave is modulated into the double-sideband frequency-agile pump pulse train (DSFA-PPT), and the continuous probe wave is up-shifted by a fixed frequency value. With the frequency-scanning of DSFA-PPT, pump pulses at the −1 st order sideband and the +1 st order sideband interact with the continuous probe wave via stimulated Brillouin scattering, respectively. Their difference of the Brillouin loss and gain spectra relates to a synthetic Brillouin spectrum with a 3.65-dB SNR improvement for a 20ns pump pulse. This work simplifies the experimental device, and no optical filter is needed.