We report a theoretical and experimental study on stimulated Brillouin scattering (SBS) suppression in a monolithic fiber amplifier with filtered and amplified pseudo-random binary sequence (PRBS) phase modulation. Theoretically, we use a time-dependent three-wave coupled nonlinear system considering both active fiber and passive fiber to describe the acoustic phonon, laser, and Stokes characteristics in a fiber amplifier. The SBS threshold power after filtered PRBS phase modulation is numerically evaluated to obtain the optimal parameters, and the time-averaged distributions of the counter-pump power, laser power, and Stokes power at different positions along the fiber length of the fiber system are simulated. Also, we established a four-stage fiber amplifier system to verify our theory. The configuration of the fiber amplifier system includes a filtered and amplified PRBS phase-modulated single-frequency fiber laser, a three-stage pre-amplifier, and a counter-pumping main stage, subsequently. 2.5 kW output power with an FWHM linewidth of 9.63 GHz is accomplished by a domestic ytterbium-doped double-clad fiber with core/cladding diameters of 20.2/400 µm. The reflectivity of the main stage is 0.049‰ at the maximum output power, which indicates the proposed architecture is under the SBS threshold. The experiments verify the accuracy of the theoretical model, which provides a reliable reference for evaluating the SBS suppression capability of the high-power narrow-linewidth fiber amplifier phase modulated by the filtered and amplified PRBS signal.