The stimulated Brillouin scattering (SBS) effect is an important factor affecting the power boost of single frequency narrow line width fiber laser amplifiers. Utilizing white noise as the radio frequency signal source, an all fiber laser system with three stage master oscillator power amplifier is designed and built by phase modulation technique. The relationship between the spectral widths of the signal light and the SBS thresholds of the fiber amplifier system is analyzed and studied. By changing the amplitudes of the white noise signal, the spectral widths of the signal can be accurately controlled, and the narrow line width quasi continuous laser output with a central wavelength of 1030.93 nm, a line width of 0.9 GHz and an average power of 90 W is obtained. The corresponding X direction and Y direction of the beam quality factors are 1.28 and 1.27, respectively. This research provides a reliable theoretical and experimental basis for the industrialization of high power single frequency narrow line width fiber lasers.