A two-stage narrow linewidth fiber amplifier with all-fiber structure based on the technique of master oscillator power amplifier (MOPA) , was theoretically simulated.The seed-signal operating at the wavelength of 1064 nm has the characters of ultra-short pulse duration (10 ps), high repetition rate (10 MHz), low single power input (20 μW) and single longitudinal mode.The stimulation model was used to calculate the gain and amplification stimulation emission (ASE) at the different pump powers and gain fiber lengths of ytterbium-doped fiber amplifier (YDFA) with a pump of 980 nm laser diode.The amplification at the different single input powers was simulated.The linear and nonlinear varieties that the output single power depended on the input single power were obtained in the parts of our two-stage amplifier respectively.The calculation results agree with the experimental phenomena, which can guide the design of the YDFA.