Abstract: In order to suppress the amplified spontaneous emission (ASE) in the low-repetition rate high-energy fiber master-oscillator-power-amplifier (MOPA) system and achieve the best amplification results, it is necessary to optimize the pump pulse width. Based on solving a set of time-dependent rate and power transfer equations, the transient response of the upper level population distribution, stored energy and ASE of the Yb-doped fiber amplifier under pulsed pump are numerically studied. And the numerical optimum pump pulse width is 793 s under specific parameters given in the paper, including the pump power, fiber length, core area, Yb-doped concentration, etc. In the experiment the ASE built-up time is measured, and the optimum value is 800 s which is found by tuning the width of the pump pulse and measuring the amplification results of the fiber amplifier. The experiment shows the validity of the numerical simulation. 