In order to further study the dynamics of relaxation oscillation during stimulated Brillouin scattering （SBS） and to avoid optical damage caused by SBS under high power lasers in applications such as fiber amplifier and fiber phase conjugate mirror，etc.，the dynamics of relaxation oscillation during SBS in fibers are studied on the basis of the SBS coupled amplitude equations using numerical simulations of finite difference methods. Meanwhile，we propose a method to suppress the relaxation oscillation. For different rise time of SBS pump pulse，the temporal and spatial variation of intensities of pump and Stokes waves is plotted as three-dimensional figures. The corresponding experiments have been conducted and the experimental results agree well with the theoretical results. From the experiments and numerical calculations it can be concluded that，by increasing the rise time of SBS pump pulse the relaxation oscillation can be suppressed effectively and the optical damage caused by SBS can be avoided consequently.