A method of realizing the wideband stimulated Brillouin scattering (SBS) slow light was proposed using double broadband pump in a single-mode optical fiber. The theoretical models of this double broadband pump SBS slow light and its pulse broadening are presented. Dispersion analyses indicate that there exists the optimum spectral separation between the central frequencies of the double pump beams with respect to the inherent spectral width of the pump laser, which makes it possible to effectively reduce the signal pulse broadening related to the group velocity dispersion. Theoretical calculations show that the SBS gain bandwidth and the signal pulse's group delay using the proposed scheme can respectively be enhanced to 1.7 and 2 times of those using just one single broadband laser of the two pump beams.