High-power operation of single-frequency Raman fiber amplifiers (SF-RFA) is usually limited by the onset of stimulated Brillouin scattering (SBS). Simulation results indicate that the output power of a single-stage SF-RFA is always low and the needed pump power is too high to satisfy. The amplifiers with multiple stages have comparatively higher output power and efficiency. Different types of fiber should be provided in different stages so that the output power could be optimized according to the attainable pump power. Taking a two-stage amplifier as an example, 100 m fiber with the core diameter of 6 μm is used in the first stage. By utilizing strain gradients along the fiber to suppress the SBS, the output of the first stage is increased to 3 W under the pump power of 32 W. The output power of the first stage is seeded into the second stage with an isolator between them. The second stage is composed by 70 m fiber with the core diameter of 15 μm. By suppressing the SBS with strain gradients, 20 W and 30 W output powers are obtained with the pump powers of 105 W and 130 W, respectively.