The pulse duration stability of stimulated Brilloiun scattering (SBS) in SF6 gas pumped by a broadband KrF laser was studied theoretically and experimentally. The dependence of the pulse duration stability of SBS on the power density stability, pulse duration stability of the pump laser and medium gas pressure was obtained. The results showed that the pulse duration stability of SBS is directly correlated with the stability of the pump laser; the pulse duration stability of the SBS increases as the stability of the pump laser does. The instability of SBS pulse duration occurrs when pulse duration and energy of pump laser were instability. Under lower pump power density, the influence of the pulse duration and pump laser energy fluctuation on the pulse duration of SBS is not ignored; but under higher pump power density, the pulse duration stability of SBS is mainly influenced by the fluctuating in pump pulse-width. The experimental results were analyzed and discussed. And for obtaining better pulse duration stability of SBS, pump laser with stable pulse duration should be used. And enhancing pump density of pump laser and medium gas pressure without other nonlinear effects are also necessary.