We suppress stimulated Brillouin scattering in an erbium-doped optical fiber amplifier for 50-ns-long transform-limited signal pulses by counter-directional pumping with a pulse burst. The pump pulse burst is codirectional with the parasitic Brillouin Stokes wave, which, therefore, undergoes cross-phase modulation and thus spectral broadening due to the intensity-modulated pump. The broadening inhibits its growth. We experimentally study the effect of pump pulse parameters and improve the SBS threshold by up to 4 dB when amplifying signal pulses at a wavelength of 1565 nm with pumping at 1536 nm.