Rapid urbanization has altered the regional hydrological processes, posing a great challenge to the sustainable development of cities. The TVGM-USWM model, a new urban hydrological model considering the nonlinear rainfall-runoff relationship and the flow routing in an urban drainage system, was developed in this study. We employed this model in the Huangtaiqiao drainage basin of Jinan City, China, and examined the impact of land cover changes due to urbanization on rainfall-runoff processes. Two urbanization scenarios were set up in the TVGM-USWM model during the design rainfall events with different return periods. Results showed that (1) the TVGM-USWM model demonstrated good applicability in the study area, and the RNS values of the flood events are all greater than 0.75 in both calibration and validation periods; (2) the proportion of impervious areas increased from 44.65% in 1990 to 71.00% in 2020, and urbanization played a leading role in the process of land cover change and manifested itself as a circular extensional expansion; and (3) urbanization showed a significant amplifying effect on the design flood processes, particularly for relatively big floods with small frequency, and the impact of urbanization on the time-to-peak of the design flood gradually decreased as the frequency of the design rainfall decreased. The results of this study can provide technical support for flood mitigation and the construction of a sponge city in Jinan City.