Implementation of pulsed-pump technique to fiber amplifier is significantly useful in the situation of low repetition rate and high energy pulses operating. The Amplified Spontaneous Emision (ASE) dynamics simulation in a pulsed-pumped ytterbium-doped double-clad fiber amplifier was presented, which provides important references about optimizing the pulsed-pump mode. By solving the rate equations and light power propagation equations in fiber using the finite elements analysis method, the simulations of ASE dynamics were carried out, including evolution of forward, backward ASE power distribution in the fiber and variations of ASE output power at two ends of the fiber in the time span from 0~740 μs after injection of pump light. Through the analysis of simulation results, the difference between forward and backward ASE powers increasing speeds and characteristics of the two kinds of ASE powers distributions dynamic in fiber were indicated.