Abstract: The suppression methods of stimulated Brillouin scattering (SBS) in high power fiber laser are analyzed. The results indicate broadening the spectrum with high speed phase modulation is one of the most effective ways to suppress SBS. With a broadband noise generator, kW level several 10 GHz linewidth fiber lasers, which are suitable for spectral beam combining, can be easily developed. On purpose of optimizing the parameters of the fiber laser, we calculate the relationship between the laser linewidth and the SBS threshold. At the same time, the effect of noise modulation parameters on spectral broadening is analyzed by numerical calculation. By broadband noise high speed phase modulation, the linewidth of the seed is broadened to 13 GHz. With a two-stage amplifying, the power is enhanced to 10 W. A 20/400 m commercial Yb-doped fiber is used in the final stage amplifier, which convinces central wavelength 1064 nm, linewidth 13 GHz, maximum power 1.06 kW fiber laser. The M2 is better than 1.2 and the O-O efficiency is 86%. During the whole experimental process, the mode instability is not observed. By broadening the bandwidth of the noise generator or enhancing the modulation depth, a higher power narrow linewidth fiber laser can be expected.