In order to increase time delay and decrease pulse broadening via stimulated-Brillouin scattering slow light, the coupled amplitude equations of stimulated Brillouin scattering in optical fibers are solved with fourth-order Runge-Kutta formula and characteristic-line mothod, the influence of the edge sharpness, magnitude and duration of injected Stokes pulse on time delay and pulse broadening factor are investigated. A method of optimizing time delay and pulse broadening factor is represented, namely, increasing the sharpness of Stokes pulse appropriately. Comparing with using Gaussian pulse as injected Stokes pulse, the similar time delay and less pulse broadening factor are obtained by this method. Theoretical analysis based on different power of injected Stokes pulse proves that improving the sharpness of injected Stokes pulse contributes a lot to reduce pulse broadening factor.