The stability of stimulated Brillouin scattering (SBS) conversion efficiency and phase conjugation (PC) fidelity are mainly depend on the leading edge of pump pulse. If the rise time of the leading edge of the pump pulse is near to the acoustic phonon lifetime of SBS medium and pump energy is well over the SBS threshold, the SBS PC fidelity will become very unstable. For pump pulse with 2 ns leading edge and CCl 4 medium with about 1 ns acoustic phonon lifetime, when introduced a small slow rising signal at the front foot of the pump pulse's leading edge, a stable SBS produced by two-cell SBS PC mirror is obtained even for pump pulse energy exceeding 500 times SBS threshold. The fluctuation of the SBS conversion efficiency is within 4%, and that of the PC fidelity is within 5%.