Using stimulated Brillouin scattering (SBS) to compress the laser pulse became more attractive in the past several years. With this method, the pulse width of ruby laser and double-frequency YAG laser output can be squeezed efficiently-(3]. We used the 5600X output pulse from a dye laser as the pump beam for SBS, the dye laser is pumped by a double-frequency YAG laser. The compressed pulse of SBS was obtained and the compression ratio is approximately 20:1. In addition, the multi-peak process of SBS was observed as well. For explanation of this phenomenon, M.J.Damzen suggests that the multi-peak effect is caused by the coupling between SBS wave and pump wave. According to this explanation, the multi-peak should be depleted one peak after another. But it is contrary to our experimental result. Other authors suggested that the main reason of the effect resulted from the amplifier and feedback of the laser. Unfortunatly this theory can not explain the situnation where no laser amplifier exists. In our opinion, this phenomenon is caused by the oscillatory character of the transient SBS process, when the squeezed pulse width is almost equal to the response time of the SBS medium.