We propose a high-gain and frequency-selective amplifier for a weak optical signal based on stimulated Brillouin scattering in a single mode fiber. To be able to satisfy the needs of high gain and high signal-to-noise ratio laser pulse amplification, different fiber lengths and core diameters are used to fulfill this experiment. In the experiment, a 430 nW (peak power) pulsed signal is amplified by 70 dB with a signal-to-noise ratio of 14 dB. The small size, high gain, low cost, and low noise of the fiber Brillouin amplifier make it a promising weak signal amplification method for practical applications such as lidar.