A model based on carrier rate equations is proposed to evaluate the gain saturation and predict the dependence of the output power of a terahertz master-oscillator power-amplifier quantum cascade laser (THz-MOPA-QCL) on the material and structure parameters. The model reveals the design rules of the preamplifier and the power extractor to maximize the output power and the wall-plug efficiency. The correction of the model is verified by its agreement with the experiment results. The optimized MOPA devices exhibit single-mode emission at ∼ 2.6 THz with a side mode suppression ratio of 23 dB, a pulsed output power of 153 mW, a wall-plug efficiency of 0.22%, and a low divergence angle of ∼6°×16°, all measured at an operation temperature of 77 K. The model developed here is helpful for the design of MOPA devices and semiconductor optical amplifiers, in which the active region is based on intersubband transitions.