To simplify the experimental equipment and improve the signal-to-noise ratio (SNR) of the traditional Brillouin optical time-domain analysis (BOTDA) system, we propose a scheme using the frequency-agile technique to measure Brillouin gain and loss spectra simultaneously. 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 −1st-order sideband and the +1st-order sideband interact with the continuous probe wave via stimulated Brillouin scattering, respectively. Therefore, the Brillouin loss and gain spectra are generated simultaneously in one frequency-agile cycle. Their difference relates to a synthetic Brillouin spectrum with a 3.65-dB SNR improvement for a 20-ns pump pulse. This work simplifies the experimental device, and no optical filter is needed. Static and dynamic measurements are performed in the experiment.