A large aperture fused silica tapered fiber phase conjugate mirror is presented with a maximum 70% stimulated Brillouin scattering (SBS) reflectivity, which is obtained with 1 kHz repetition rate, 15 ns pulse width and 38 mJ input pulse energy. To the best of our knowledge, this is the highest SBS reflectivity ever reported by using optical fiber as a phase conjugate mirror for such high pulse repetition rate (1 kHz) and several tens of millijoule (mJ) input pulse energy. The influences of fiber end surface quality and pump pulse widths on SBS reflectivity are investigated experimentally. The results show that finer fiber end surface quality and longer input pulse widths are preferred for obtaining higher SBS reflectivity with higher input pulse energy. Double passing amplification experiments are also performed. 52 mJ pulse energy is achieved at 1 kHz repetition rate, with a reflected SBS pulse width of 1.5 ns and a M(2) factor of 2.3. The corresponding peak power reaches 34.6 MW. Obvious beam quality improvement is observed.