We present a model for longitudinal mode competition in coupled-cavity (CC) terahertz (THz) quantum cascade lasers (QCLs) by using a scattering matrix method and multimode reduced rate equations (RREs). The dependence of the mode selection and tuning characteristics on various device parameters is systematically investigated, including the net waveguide loss, the optical length of the passive cavity, and the heat-sink temperature for different relationship between the active and passive cavity lengths. The changes in eigenmode frequencies due to variations of device parameter are calculated before solving the RREs. The mode selection and tuning results obtained from solving the nonlinear RREs could be well explained by the linear scattering matrix analysis. The mode tuning process simulated by the proposed model is compared with experimentally measured data, yielding good agreement. Comprehensive study of the influence of the key device parameters on the performance of CC THz QCLs provides potential design rules for single-mode operation with either wide frequency tunability or high stability.