A continuous laser diode （LD）end-pumped Nd∶YVO4 laser amplifier within a MOPA structure has been designed.Based on the rate equations describing the radiation amplification process,a computational model has been established which shows a good agreement with the experimental results for the kHz pulses.It is demonstrated both experimentally and theoretically that the amplification tends to a steady state with the increasing of the input pulse frequencies.Using this model,we can conclude that an optimal gain length exists to obtain maximum amplification for a given MOPA structure.In our experiment,this length is found to be about 8.5 mm.