The authors present a study on the effects of design parameters on the performance of terahertz quantum-cascade lasers by using a Monte Carlo method, including essential scattering mechanisms and the hot-phonon effect. Three design parameters, i.e. injection and extraction barrier widths and doping concentration, are investigated. In the range of the three design parameters we used, simulated results show that the current density increases monotonically with the decrease of barrier widths and the increase of doping concentration. The calculated gain is more sensitively dependent on the injection barrier width and doping concentration. Thicker extraction barriers, i.e. from 39 to 48 Å, are acceptable.