By using the six temperature model theory on the kinetic process in a CO2 laser system, we build a mathematical model to calculate output characteristics of Q-switched CO2 laser power amplifier. Theoretical analysis as well as numerical calculation is carried out, and the effects of parameters such as beam split ratio on output pulse characteristics and output spectra are discussed. The results show that the Q-switched CO2 laser power amplifier has a critical gain length and a critical beam split ratio, below which no laser output can be obtained. The laser pulse waveform, peak power, pulse width, and output spectra of the Q-switched CO2 laser power amplifier are all effected by the beam split ratio and pumping electron density. The less the beam split ratio, the greater the output Q-switched laser pulse width, and the lower the laser peak power. The Q-switched CO2 laser power amplifier utilizes the high gain characteristic of Q modulation. By controlling the low power branch of Q-switched elements, we realize the Q-switched pulse CO2 laser output with high average power. The problem that Q-switched CO2 laser power amplifier is difficult to operate at high power is well solved.