The influences of temperature distribution on stimulated Brillouin scattering (SBS) in high power single-frequency fiber amplifier are studied, based on the rate equations combining with SBS. The results indicate that temperature gradients along a fiber can broaden the SBS gain profile and thereby suppress SBS. The threshold of pump power and the output power of amplifier can be increased significantly by cooling fibers around the output port of amplifier actively. The length and location of fibers cooled to suppress SBS have the optima, which are influenced by pump power, temperature distribution and length of total fiber in amplifier. The threshold of pump power and output power of amplifier can be increased more than 2 times under the optimum condition.