Based on discrete algorithm of propagation-rate equation, the ASE dynamic behavior of Er3+/Yb3+co-doped double-clad fiber amplifier under both continuous and pulse pumping is studied. The reason for different change of the ASE output power with time is analyzed as well. The results show that the time and output power value of ASE reaching steady state under continuous pumping depend on the pump power, and the increase of ASE output power corresponds to the decrease of the inverted population of Er3+/Yb3+. This study also shows that the length of the fiber under pulse pumping affects significantly the saturation of the forward ASE output power, but does not affect that of the backward ASE output power.