An efficient flood forecasting system can provide useful advance information for evacuating people in order to mitigate potential disaster. In Taiwan, a kinematic-wave approximation of the full dynamic-wave equations is usually adopted in upstream and midstream steep channel reaches to avoid numerical instability when performing a flood forecast. Although the kinematic-wave approximation does provide a convenient simulation, questions arise with respect to its applicability and accuracy. In this study, numerical algorithms were developed to investigate the deviations of the hydrograph peak discharge and the time to peak discharge using the dynamic- and kinematic-wave methods. A series of numerical experiments were performed to investigate the hydrograph deviations using these two methods. Numerical results show that the flood-peak attenuation generated using the dynamic-wave method is more significant than that using the kinematic-wave approximation, and also that flow hydrographs generated using the dynamic-wave method always precede those using the kinematic-wave approximation. Regression results demonstrate that channel slope and roughness dominate the flood hydrograph attenuation and translation. Nevertheless, hydrograph deviations between these two methods were found to be small for a channel slope larger than 0.001, which can therefore be recognized as a criterion for ensuring the precision of the kinematic-wave approximation.