By solving a set of time-dependent equations, the characteristics of the ytterbium-doped double-clad fiber amplifier are presented. Besides the steady state in the fiber of the upper-state population, pump power and amplified spontaneous emission without the input signal, the dynamic characteristics of the high power Gaussian pulse amplification like the evolution of pulse waveform distortion, upper-state population distribution and stored energy and pulse energy of the amplifier under the forward and backward pump, are simulated. The relations between the output pulse energy of the amplifier and the different input pulse peak power or pump power are also discussed. The models and results can provide important guide for the design and optimization of the high power pulse amplification.