On the basis of the multi-longitude theory of stimulated Brillouin scattering (S BS), a group of coupling wave equations without limitation to the mode separatio n of a laser was deduced while the random initial phases of the multi-longitudin al modes were introduced for SBS pumped by a free-operating laser. The dependenc es of broadband SBS threshold on the bandwidth of the laser, the number of the l aser modes, the mode separation of the laser, the linewidth of Brillouin, and th e ratio of the SBS interaction length to the laser coherence length were discuss ed in detail. And the theoretical results were consistent with the experimental results reported.