High peak power, narrow linewidth sources continue to be in high demand. Fiber amplifiers are a compelling option to scale peak power of long 100-ns-pulses because of their compact size and robustness. Unfortunately, stimulated Brillouin scattering (SBS) limits peak power of narrow linewidth fiber sources causing instability. We demonstrate SBS suppression for 130-ns pulses from a 5 MHz linewidth seed laser in a fiber amplifier by using tapered fiber with large 50 µm diameter core in the output. The longitudinal change in the core diameter induces frequency shift in the SBS gain peak and the back-travelling Stokes wave is suppressed towards smaller core. We reach 2.2 kW peak power with 18.7 dB polarization extinction ratio and record breaking 4 kW peak power by exciting both polarization states of the polarization maintaining tapered fiber. The output beam quality equals to single mode fibers with M2 = 1.08.