In the pulsed fiber amplifiers with repetition frequency of several tens kHz, amplified spontaneous emission (ASE) is easy to build up because of the low repetition frequency and weak pulse signal. The ASE rises the difficulty to amplify the weak pulse signal effectively. We have demonstrated an all-fiber preamplifier stage structure to amplify a 40 kHz, 10 ns bandwidth (FWHM) weak pulse signal (299 μW) with center wavelength of 1062 nm. Compared synchronous pulse pump with continuous wave(CW) pump, the results indicate that synchronous pulse pump shows the better capability of increasing the output power than CW pump. In the condition of the same pump power, the output power of synchronous pulse pump is twice as high as CW pump. In order to suppress ASE, a longer gain fiber is utilized to reabsorb the ASE in which the wavelength is shorter than 1062nm. We amplified weak pulse signal via 0.8 m and 2.1 m gain fiber in synchronous pulse pump experiments respectively, and more ASE in the output spectra are observed in the 0.8 m gain fiber system. Due to the weaker ASE and consequent capability of higher pump power, the 2.1 m gain fiber is capable to achieve higher output power than shorter fiber. The output power of 2.1 m gain fiber case is limited by pump power.