We propose a novel (to our knowledge) driving scheme to suppress the stimulated Brillouin scattering (SBS) effect in master oscillator power amplification (MOPA) systems based on an external high-order phase modulation. Since seed sources with the linear chirp can uniformly broaden the SBS gain spectrum with a high SBS threshold, a chirp-like signal was designed by applying further editing and processing to the piecewise parabolic signal. Compared with the traditional piecewise parabolic signal, the chirp-like signal has similar linear chirp characteristics and can reduce the driving power and sampling rate requirements, enabling more efficient spectral spreading. The SBS threshold model is constructed theoretically based on the three-wave coupling equation. The spectrum modulated by the chirp-like signal is compared with the flat-top and Gaussian spectra in terms of the SBS threshold and the bandwidth-distribution normalized threshold, and a considerable improvement is demonstrated. Meanwhile, the experimental validation is carried out in a watt-class amplifier based on the MOPA structure. At a 3 dB bandwidth of ∼10 GHz, the SBS threshold of the seed source modulated by the chirp-like signal is improved by 35% compared to the flat-top spectrum and 18% compared to the Gaussian spectrum, respectively, and the normalized threshold is also the highest among them. Our study shows that the SBS suppression effect is not only related to the power distribution of the spectrum but also can be improved by the time domain design, which provides a new idea for analyzing and improving the SBS threshold of narrow-linewidth fiber lasers.