This study modifies a Global River-flow model (GRiveT) to more realistically represent groundwater and river-flow processes and examines the effects of these modifications on the reproducibility of the hydrological processes. These modifications include assigning calibrated spatially distributed current speeds and implementing a groundwater scheme. A current speed calibration method is proposed to eliminate river discharge phase differences (RPDs) between the observation and the simulation. We performed nine-year integrations of the modified version of GRiveT. The experimental results were then compared with the observed data for 70 of the world’s major rivers. The proposed calibration method provides reasonable calibrated speeds that eliminate RPD for most of the 70 rivers considered. The calibration significantly improves the river discharge correlation coefficient and phase difference and improves the terrestrial water storage (TWS) correlation coefficient and phase difference to a lesser extent. However, there was little improvement to river discharge and TWS amplitudes. The implementation of the groundwater scheme improves river discharge and TWS correlation coefficients and phase differences for experiments without calibration. The calibration can compensate for the disadvantages of not implementing the groundwater scheme.