Some analysis of the transient response of the Yb-doped fiber amplifier are performed by solving a set of time-dependent rate and power transfer equations based on finite-difference method. Meanwhile, the variation of time to reach the steady state for upper level population distribution, the forward and backward amplified spontaneous emissions (ASEs) and stored energy on the system parameters including pump power, fiber length, Yb-doped concentration, and core area are numerically simulated, respectively. The results show that, by optimizing pump pulse width, stored energy can reach or even exceed the steady state value of continuous wave (CW) pump. By increasing Yb-doped concentration and core area, stored energy is increased, the ASE is suppressed and the ASE built-up time is postponed. In addition, the experimental results show the validity of the theoretical ASE built-up time. The obtained results can provide important guiding for the optimization of pump pulse width and fiber parameters.