Suppression condition of stimulated Brillouin scattering (SBS) in high-power single-frequency fiber amplifier is analyzed and simulated in this paper. The set of differential equations for an fiber amplifier with pump, signal and the first-order Stokes, taking into account effects of thermal gradients caused by heat generation, is presented.The influence of pump powers, convective coefficient, fiber lengths, and detuning of the Stokes frequency from exact SBS resonance on SBS gain (G) is studied under unidirectional and bi-directional end pumps. Compared to forward pump and bi-directional pump schemes, backward pump scheme offers the least gain (G), which can be further reduced through decreasing convective coefficient and fiber lengths. When total pump power is 1 kW, gain (G) of three-segment distributed pumping scheme is higher than the SBS gain threshold value. The results show that the backward pump scheme has advantage over other pump schemes in suppression of SBS, and the SBS is not a limiting factor to single-frequency power extraction from fiber amplifiers for a properly temperature variation and sufficiently short amplifier length.