We propose the insertion of a saturable absorber (SA) in a nanosecond double-pass laser amplifier as an amplified spontaneous emission (ASE) suppressor. To analyze the influence of the SA, a theoretical model is developed. One-dimensional simulation results show reasonable agreement with measurements in terms of the output energy and temporal pulse shape. For our amplifier parameters, when an SA of initial transmission 0.5 is inserted, the simulation anticipates the ASE to be reduced by a factor of 0.37 while the output pulse energy is maintained.