Based on simulated annealing algorithm, the terahertz composite achromatic quarter-wave plate is designed for two frequency bands, 0.2~2.0 THz and 0.2~3.0 THz bands. Remarkable design results (retardation deviation is 2% from 0.2 to 2.0 THz and retardation deviation is 4% from 0.2 to 3.0 THz) are got. The influence of different numbers of quartz plates on the key parameters of the quarter-wave plate, such as achromatic performance, thickness and loss is analyzed. It is shown that with the increase of the number of quartz plates, the achromatic performance of the quarter-wave plate will be improved and phase delay detuning will also be reduced; however, the thickness of the quarter-wave plate is increased, leading to the increase of the loss. It is also shown that the optimized quartz plate number is five, with which good achromatic performance can be got, and the thickness and the loss are also practical for THz application.