Phonon amplification in low-dimensional material structures has primary important applications for engineering instrumentation applications such as phonon spectrometers, phonon lasers, ultrafast optical modulators as well as other devices based on magneto, acoustoelectric and thermal effects. In this paper, we report our theoretical calculation of the acoustic phonon rate in a parabolic semiconductor quantum well. Using the method of quantum kinetic equations, we have found the expression for the acoustic phonon growth rate and the condition for this phonon increase. The analysis results for the gain factor for the acoustic phonons depend on the temperature, amplitude and frequency of the laser field. We numerically calculate the rate of acoustic phonon excitation by the absorption of laser field energy at different temperatures.